Agree with this. DS was lucky and preschool started things rolling, but it's always a slow process. He had in-school assessments then hearing tests, and eventually speech and language referred him for an autism assessment. That happened after he'd started reception, but because he was already on the radar, the school made adjustments, ensured he had lots of TA support, and started him with an IEP or whatever the informal plans were called ten years ago. You shouldn't need a diagnosis or an EHCP to get support. DS was still not toilet trained (dry but not poos) but the school were fine as I had a diary of all the actions we'd tried over the years.
Once he got a diagnosis the school then got extra funding (always a year retrospectively, and never for the full hours) - so it's to their benefit to speed things up if they can, but that shouldn't stop them providing whatever your DC needs in the meantime.
I've been there and back so many times - meltdowns, poo smearing, demanding we retrace our steps to do things differently, aggression to other children, again and again.....! Primary school is so hard! I know they're all different, but DS is 14 now and life is really so easy! He sometimes struggles socially and/or academically, and occasionally has minor meltdowns where he doesn't think I support him with social issues (i.e. he doesn't seem able to listen to advice) but I never imagined how much better things would be. Hang in there. Demand support from the school, get the diagnosis when your turn comes - and then apply for the EHCP and anything else you think she needs - but hopefully the time will fly by and your school will be there with you.
Interestingly - I think CAMHS involvement is maybe a postcode lottery? In our county they would never be involved in anything like this, and are there to support older children with serious mental health issues. I've never heard of them being used to support primary school children (except maybe very serious cases which I would know nothing of) - and 'routine' situations where parents are looking for support with ASD, ADHD, OCD or whatever would be dealt with via paediatricians, speech and language, and maybe Ed Psych reports.
Can you ask your GP for a paediatrician assessment? Or apply online via your LA for a non-school referred EHCP? Worth looking at other options. And maybe talking to the National Autistic Society helpine for advice?
Good luck. You're doing all you can, I hope it works out for you soon.