Also OP to answer your question about diagnosis, do the NHS AQ-10 on her behalf. Take this to the GP, explain her behaviours. They will make a referral if she scores enough on the AQ-10.
You can also do the AQ-50 although they usually send you a self report form, which will likely contain this anyway, and then you post this back to them.
When you get to the assessment side of things there's a history interview, as she's young really it'll be about her present struggles and presentation. They are aware girls score higher at masking compared to boys.
Then she will be invited to do further assessments, the most common tool is called an ADOS, and it's a series of different tasks which screen for things like apraxia, aphantasia, body language and non-verbal communication, social understandings etc but for children it is mostly play based.
They're essentially looking for deficits in 3 key areas.
For children as well they may request feedback from other agencies or wish to observe her in setting. She might get on well with other kids at school and be a dream for teachers but for someone with a keen eye it's easy to pick up on things like structured play over imaginative play, social cognition etc that teachers won't necessarily be keeping an eye out for in someone who is well behaved and flies under the radar.
I don't know if this is the sort of answer to your question that you were wanting, and I know it will vary region to region but I hope it tells you what you can expect if you do decide to proceed.