Thanks for all the feedback. We are in Florida, and we have an IEP for her already, but for speech. I will have to get that amended for sure.

My children were both diagnosed at 3 and they can now do it even younger. If you need a specialist a psychiatrist is good, or a neurologist would work as well.

A good developmental pediatrician can also give you guidance about next steps. Are you in the States?
If so, with a diagnosis you should be able to get an IEP to create goals for your child at school.

Thank you both! We go back to the new psychologist on Monday and I will ask her about the DSM-5.
Jayney, she goes to a small private school and receives a state scholarship because of her speech delays. I have been told that the scholarship amount will go up significantly if she has an official diagnosis, but I'm wavering about making it fully "official" because I don't want her to be pre-judged by teachers as she gets older. So far we have had wonderful teachers who make any accommodations we need, but I know at some point she will need more than just flexible teachers!

My daughter was diagnosed with Autism/AS at age 5. Her school and her GP were very much behind us and we received the support at this age as for Lily is would have been too early to diagnose before.
Will the school get behind you?
Wishing you the very best. x