If you can afford to see an occupational therapist so that her sensory needs can be assessed then that could be a good starting point. It costs around £450 in my area to have a really detailed assessment (my DD’s took around 6 hrs over a couple of sessions)
This was massively helpful as it meant that school had to give sensory and movement breaks.
My DD did go on to be diagnosed with autism, but not until she was 9 as she has relatively good social skills - good eye contact, lots of facial expression, asks questions etc - and seems very confident in some social situations . There were no concerns at nursery age, or in school for the first few years - although she was a “very sensitive” baby/toddler/child at home.
She can tolerate some noisy environments but not others, or cope with one on one occasion but not on another, it’s variable depending on the activity and what else is going on for her on that day.
You said your DD doesn’t have any other markers for autism - the difficulties need to exist across three areas. Social and communication, and sensory are two of them, which you already have signs of.
The third is - and someone else can probably explain this much better - repetitive behaviours/special interests.
This can be harder to spot in girls. My DD collects soft toys - didn’t really stand out in a younger child of course ! - and has always had a tv series on the go that she watches again and again, where she knows everything about the characters and mentions them a lot. Which can be usual, again, but there is something unusual about the level of it and degree of knowledge/obsession, if you are watching for it.
She also doesn’t flap - but she does cartwheel repetitively and stand on her head, something else that blended in and didn’t stand out as unusual for a long time - she also clicks her fingers when stressed, I hadn’t noticed really, it’s hard to see things when you are so close up.
I didn’t notice or put this together until she was 8 and it became clear that there was something wrong - and still, it seemed to present as a mental health problem, I brushed it aside when a paediatrician first asked me if I thought she was autistic and gave a confident “no, she has no special interests”.
I am telling you this just because the pathway to diagnosis is years long in some areas. If you have your DD put on and she isn’t autistic then this might become clear before an assessment date comes, you could take her off the list. You have nothing to lose there.
But if your DD is, it’s likely that any difficulties will have become more obvious by then.
I desperately wish someone had raised this as a possibility so much sooner for us. It would have saved so much heartache and confusion later on, when no-one knew what was happening, we were being fast tracked to CAMHS - due to risk to herself - and I had an 8 year old child who was suddenly in crisis.
And the signs were there from early on, and would have been visible someone who had known what they were looking for - if I’d spent time around other parents with autistic girls then I think I’d have recognised it so much earlier, or the other parents would.