Autism signs in 4 year old girl

I'm a first time mum so not really sure how much of this is normal toddler behaviour and/or if it could be signs of ASD but I'm wondering whether or not to ask about diagnosis as if my daughter does have ASD then I'd rather she had support in place as soon as possible after starting school in September.

I've tried reading around online but it really hasn't helped so please could any of you tell me if this sounds like your daughter who is on the autistic spectrum:

Very rigid over daily routines and gets extremely upset if there are any changes, even very minor ones, like walking even a slightly different route to or from somewhere familiar.

Is a perfectionist over things that she is learning and gets very upset if she gets wrong or even if mummy or daddy say the wrong word sometimes

Likes to control everything in her world. I should say we give her as many options as possible so that she feels she does have a bit of control but if it's something she is being 'told to do' or doesn't want to do then she has a tantrum. 

Has frequent tantrums at home, which can get physical, including hitting and kicking. She has been going to preschool and we have been pulled aside a few times during the year for incidents of kicking other pupils, and she stamped on a teachers foot. She refused to apologise for both and ended up having her boots taken away and being sent out of the classroom. The head of nursery has been working and there haven't been any recent incidents.

Can get a bit overwhelmed by certain noises like mowers, the hoover, hand dryers out and about although she is getting a bit better with this now.

Likes to put things in her mouth a lot, loves cuddles (more so if she initiates them), but frequently avoids eye contact.

Is hyperactive most days and struggles to sleep unless she is very tired.

Is very intelligent, learnt the alphabet before 2 and was reading at 2. Is also a very good counter and has been able to count about 100, do basic maths, and correctly use basic science concepts like gravity, displacement and upthrust since 3. Is very interested in learning as much as possible about certain topics, particularly science, and space.

Likes to play with toys in the same ways and can get upset with other boys and girls if they don't share that vision. Struggles to take turns, and share.

Holds on to go to the toilet even though she has been fully toilet trained for a while. She won't go until she's desperate, and will hold on for hours.

She has been at preschool part time so for just 3 hours a day so far but I'm a bit worried about how she'll manage with full-time. My husband thinks I'm over thinking things and should see how it plays out.

I may have missed some stuff but think I've included the most important points. The rituals that she has can take up large chunks of the day and the main thing for me is that she is happy.

Thanks for reading, sorry for the long post but does anyone think that I should seek a diagnosis for my daughter or that I'm overreacting and this is all toddler behaviour anyway? Anyway thoughts or advice is much appreciated.

Thank you ️