Apologies in advance for the long post. It is a bit of a bugbear of mine that professionals often don't mention these things and getting correct information from LAs can be difficult.
Anne, we have a highish household income. But having DC with additional needs is bloody expensive. We get DLA for all 3 DS' and while we could afford not to claim it and my carer's allowance it would mean cutting back. DC would get fewer experiences - holidays, days out, clubs etc. We wouldn't be able to have our cleaner so I would have less time to focus on DC's needs. I couldn't randomly spend £££ without thinking on all the things I think might help but don't - Privacy Pop, various lighting, dream pad pillow... We have also found it acts as evidence of need e.g. Carer's tickets for museums etc., respite clubs, charities, blue badge, CEA card for free carer's tickets at cinemas, disabled railcard, disabled bus pass... If I was you I would claim it, it is to cover the extra expenses for DD's benefit. For us it doesn't cover the additional costs, but it helps. David Cameron claimed it for his son, it is not means tested for a reason. Not relevant to you but DLA for 2 year olds gives access to funded nursery hours.
A carer's assessment from the LA opens doors too. Via that I learnt of a sensory playgroup held at a local special school which let my then 7 year old DS1 attend. And of a local authority carer's grant which we got for some new garden furniture. It also means we are on their books for when we need them e.g. It made getting some emergency respite easier. It was towards the top of my to do list when we moved LAs. An assessment from the disabled children's team for DC does similar. Again not relevant for you but social care can access funded nursery hours.
Merlin's Magic Wand covers more than just theme parks - Warwick castle is included, Madame Tussaud's, Sea Life centres, London eye, London (and other) dungeons etc.
Yes, still get a CAMHS referral. Your DD is then known to them in case you need them in the future - or is there anything you need now well CAMHS version of now anyway. Also, not everyone accepts private diagnoses unless the HCP also works in the NHS.
Are school meeting DD's needs? If not then you could go down requesting an EHCP needs assessment. Has your DD had an Ed Psych assessment? School could ask for the ASD outreach team for support.