Frazzled Mum - 4.5 year old girl autism?

I don't think those are limited to just girls tbh. Generally though you could be describing me in my childhood there. The good news is that some of those behaviours is actually a result of anxiety second hand from the ASC itself, and that means they can be improved with healthy and compassionate coping techniques. If I engage my own memory for a moment I can run down the most likely mechanism behind a few key points:

EH123 said:

Struggles when things don't go as she expects. Very rigid in her expectations - easily throws a tantrum when things don't go as she has planned.

We teach children from day one that they should have a routine then when they take that literally we scold them for being "inflexible". Which flows into the point about hypocrites next.

EH123 said:

Follows rules/processes religiously and will point out if anyone is not following properly.

She has a good sense of fairness, and expects everyone to be held to the same standard as she is, and especially not be a hypocrite if the person breaking rules has been one to bring them up before. "Do as I say not as I do" is anathema, and causes anxiety.

EH123 said:

Very sensitive to smells - often talks about smells and tells people they smell or highlights bad smells. 

Again we cannot teach children to adhere to a behavior in this case honesty and then scold them when they are honest. White lies are a social skill that is often learned later in autists if it is at all.

EH123 said:

Doing well at school. No concerns there, but they have been working on her understanding of emotions for a while now as she struggles with regulating her emotions.

Seems to potentially mask at school, then explode when she gets home. 

This usually results from background stress at constantly trying to live up to the fluctuating expectations of everyone else and then some how "failing" too regardless.

EH123 said:

She will get fixated on baking a cake for example, and will not forget it and will go on about it constantly and no amount of explaining why we can't do it that second helps deflect the situation. She will then get really angry and not listen or understand what we have said. 

She has literal thinking, if you don't want to do it now, don't say nebulously "later". She wants that structure to feel secure, so set a date/ a timer/ whatever and then stick to it and do the promised activity. That will help.

EH123 said:

Went into the poundstore as she wanted some bath crayons.

"Mummy, where will they be?"

"I don't know Elsie, we just have to keep are eyes open and look out for them" "But Mummy, I don't know how to do that, I can't stop blinking"

Again, literal thinking, try to avoid nebulous phrasing that can confuse her and, introduce similies and metaphor later on when other language skills develop. She is still just year R and a lot of kids aren't linguistically profient at that age either, autism or not.

EH123 said:

Food wise - she is ok at eating but she changes her mind about what she likes constantly and if I chop her toast in the wrong shape, or give her the wrong coloured plate - all hell breaks loose. I think at nursery they used to ask that she at least tried the food, so now when I say she hasn't eaten enough dinner yet she fixates on the words "But I tried" thinking that means she has had enough. The other day - I said, you must eat 5 more pieces of chicken - she got one piece and broke it into 5! So cheeky, but her logic is incredible.  She saw a You Tube video that said pizza was unhealthy, so now she won't touch it.  I also say to her "Make sure you eat your chicken as it makes you grow" She has decided she doesn't want to grow, so now won't eat chicken. 

She's still developing preferences which is very natural for any child just she is doing it though an autistic rather than allist lens.
She's also clever enough to figure out how to bend rules without breaking them, because she neither wants to do a thing nor get in trouble for it. That's top tier problem solving and tbh I think you should encourage it.
Have you thought of explaining that things said on TV is just junk so she knows to be healthily skeptical about the things she's told? Ie, it's not that eating piza is unhealthy, it's that eating nothing but pizza is unhealthy, etc?

But really, remember she's just 5, she's not gonna stay like this when she's 25.
I used to be a lot more rigid until I slowly learned I could do whatever I want (within reason, I've not robbed a bank) and the sky wouldn't fall down for it, and that the social rules of non autists are just silly games to be played to keep the interactions smooth.

I don't think those are limited to just girls tbh. Generally though you could be describing me in my childhood there. The good news is that some of those behaviours is actually a result of anxiety second hand from the ASC itself, and that means they can be improved with healthy and compassionate coping techniques. If I engage my own memory for a moment I can run down the most likely mechanism behind a few key points:

EH123 said:

Struggles when things don't go as she expects. Very rigid in her expectations - easily throws a tantrum when things don't go as she has planned.

We teach children from day one that they should have a routine then when they take that literally we scold them for being "inflexible". Which flows into the point about hypocrites next.

EH123 said:

Follows rules/processes religiously and will point out if anyone is not following properly.

She has a good sense of fairness, and expects everyone to be held to the same standard as she is, and especially not be a hypocrite if the person breaking rules has been one to bring them up before. "Do as I say not as I do" is anathema, and causes anxiety.

EH123 said:

Very sensitive to smells - often talks about smells and tells people they smell or highlights bad smells. 

Again we cannot teach children to adhere to a behavior in this case honesty and then scold them when they are honest. White lies are a social skill that is often learned later in autists if it is at all.

EH123 said:

Doing well at school. No concerns there, but they have been working on her understanding of emotions for a while now as she struggles with regulating her emotions.

Seems to potentially mask at school, then explode when she gets home. 

This usually results from background stress at constantly trying to live up to the fluctuating expectations of everyone else and then some how "failing" too regardless.

EH123 said:

She will get fixated on baking a cake for example, and will not forget it and will go on about it constantly and no amount of explaining why we can't do it that second helps deflect the situation. She will then get really angry and not listen or understand what we have said. 

She has literal thinking, if you don't want to do it now, don't say nebulously "later". She wants that structure to feel secure, so set a date/ a timer/ whatever and then stick to it and do the promised activity. That will help.

EH123 said:

Went into the poundstore as she wanted some bath crayons.

"Mummy, where will they be?"

"I don't know Elsie, we just have to keep are eyes open and look out for them" "But Mummy, I don't know how to do that, I can't stop blinking"

Again, literal thinking, try to avoid nebulous phrasing that can confuse her and, introduce similies and metaphor later on when other language skills develop. She is still just year R and a lot of kids aren't linguistically profient at that age either, autism or not.

EH123 said:

Food wise - she is ok at eating but she changes her mind about what she likes constantly and if I chop her toast in the wrong shape, or give her the wrong coloured plate - all hell breaks loose. I think at nursery they used to ask that she at least tried the food, so now when I say she hasn't eaten enough dinner yet she fixates on the words "But I tried" thinking that means she has had enough. The other day - I said, you must eat 5 more pieces of chicken - she got one piece and broke it into 5! So cheeky, but her logic is incredible.  She saw a You Tube video that said pizza was unhealthy, so now she won't touch it.  I also say to her "Make sure you eat your chicken as it makes you grow" She has decided she doesn't want to grow, so now won't eat chicken. 

She's still developing preferences which is very natural for any child just she is doing it though an autistic rather than allist lens.
She's also clever enough to figure out how to bend rules without breaking them, because she neither wants to do a thing nor get in trouble for it. That's top tier problem solving and tbh I think you should encourage it.
Have you thought of explaining that things said on TV is just junk so she knows to be healthily skeptical about the things she's told? Ie, it's not that eating piza is unhealthy, it's that eating nothing but pizza is unhealthy, etc?

But really, remember she's just 5, she's not gonna stay like this when she's 25.
I used to be a lot more rigid until I slowly learned I could do whatever I want (within reason, I've not robbed a bank) and the sky wouldn't fall down for it, and that the social rules of non autists are just silly games to be played to keep the interactions smooth.

EH123

EH123 said:

First step in the process is in progress - her teacher has arranged for their SENCO teacher to observe Elsie in class.  We then have a meeting at the school with her class teacher and the SENCO teacher to discuss further in a weeks time.  I strongly expect that they will not see a whole lot of what we experience at home, because she masks so well. But will be interesting to see. 

If they need more evidence maybe you can give them a list of observations like you just mentioned as I strongly recognised my own chilldhood traits as you described in your post, and I was diagnosed way back over 20 yrs ago when they knew even less about autism than they do now.