(Taking the point that girls present very differently to boys but here's my 2p worth. I've been very precise about language and terms for once so hopefully you can relate it to your own HCT)
DS is also 'atypical' and it was a long, hard fight to get any type of dx for him. Eventually he went through the Autism Diagnostic Observation Schedule (ADOS), which was run jointly by a Consultant Pead and SALT at the Community Child Health Centre of our local children's hospital - which everyone refers to as 'the communications unit'. It was a videoed play-based assessment which lasted around 2.5 hours.
The video is then analysed and marked. If the DC 'hits' enough of the markers, then there is an automatic diagnosis of ASD. If they don't, then they don't have an ASD dx - it is very cut and dried.
Because my DS didn't hit all the markers, he doesn't have ASD. He has a dx of 'Social Communication disorder or delay'. However, he was just under the threshold for many of the markers, so it is clear he isn't NT and many of the strategies for ASD are relevant and helpful to him. In fact, I sometimes describe him as ASD as a kind of short-hand, depending who I'm speaking to.
Because we'd had such a delay in dx and accessing help, the local Spectrum team were involved in supporting DS at nursery, however when his dx was not ASD they tried to wriggle out of that pretty quickly. Once he got to school he 'transferred' into visiting teacher support and most of his help is now school based, he has 5 hours additional support but is fairly mainstreamed.
So - in conclusion:
dx isn't always important, it depends how flexible your school and healthcare trust is.
Psychologists don't dx as ASD is 'medical' for want of a better word - they can refer and support in school and are usually the access point for further support (here in Scotland anyway) but to get a dx you have to push for a pead referral
Your DS may or may not be on the spectrum, but you can use techniques for children on the spectrum to support her.
School I can't comment on as the system is different in Scotland.
HTH and sorry its so long!