You could ask for her to be assessed for an EHC plan, as a PP has said; but social care is a parallel system. As PP have said, if I were you, I'd ask for an assessment of need for social care and support for DD from the social services disability team - they may be called the Transition Team (16 - 25) or the 0 - 25 service where you are? Social services have different criteria to the mental health team. I am not a professional, but I find it difficult to believe that if your DD is entitled to DLA care and mobility at the highest rate, she won't meet the criteria for social care and support?
The assessment of her should be carer blind - ie they should assume that nobody is going to do anything for her by way of care, so how would she meet the outcomes?
"The desired goals and outcomes may include being able to:
eat properly
look after your personal hygiene
go to the toilet
dress yourself
be safe at home
keep your home clean and safe
see family and friends
go to work, volunteering, education or training
use services in your area"
If she could not meet two of the outcomes (and I would question be safe at home, if she burns herself regularly for a start), then she would meet the criteria for social care. They should also consult with you, as her carer and you can do it, not in her presence. Insist that you do not want to do any of her care (and in law, you are under no obligation to care for an adult) - you want to work, pursue education, health appointments, leisure activities, etc. Tell them, you want her to go into supported living (because what will happen to her in the event of you being in hospital for some time, or after your death) and its better to choose somewhere nice for her now, than leave it to the LA, on the day of your death - when they will choose the cheapest or what has a vacancy? Or at the very least, insist on respite - its assessed as being for her benefit, although the respite is for you!
They can send carer(s) into your house to do her cooking, laundry, washing up, etc - they won't do yours, because its in respect of her! They can also take her out to leisure activities like the cinema or shopping, whatever a "normal" adult might do in their spare time - which would also give you respite.
Tell them exactly how it is! If you give any indication, you will care for her, they will leave you to it, because it saves them money.
Finally, at the same time, ask for a carer's assessment in respect of yourself. You could ask for a cleaner for instance, to give you time to spend with DD; or a carer while you attend health appointments, etc, or respite.