Hi Hon,
I'm in Australia and the system is different. I was born in Liverpool UK BTW!
The NHS can be excruciatingly slow but very good when it gets started.
You need to empathise to the GP that this is real and your daughter needs help. Being an uncommunicative autistic may be a problem, but there is a link between autism and TG and it is well recognised. I believe each NHS region has centres of referral for TG and you need to get a link into them. Be insistent with the GP, particularly if they have never dealt with TG before.
Read through and download the Standards of Care. (SOC7) from WPATH.
www.wpath.org Take them with you. Also they will give you comfort in reading them. We are not mentally ill, we are transgender and there is a path to follow to allow us to live normal happy lives. It's quite simple! But can be a minefield.
Now personal support. This has probably been a shock and your maternal instinct has leapt in. You may question later if it is your fault etc. How to deal with family and friends etc. Is my daughter a real woman? Yes she is.
Are TG people (often called trans*people) odd or restricted in life? Well I'm a A/Prof of Medicine, there are lawyers, businessmen and women on this site. We didn't ask to be trans* we just are. We are normal men and women. Just as your child is.
Being trans* is hard, but when we are accepted and can be our true selves life is wonderful. Your daughter can have a full, normal and very happy life; as she deserves to have. And you deserve to be a very proud Mum.
Cindy