@JustGotToKeepOnKeepingOn Not only are waiting lists extremely long (and post diagnosis help minimal), her GP will probably be loathe to add to it, as there isn't actually a problem here. I got a late diagnosis (thought autism, was ADHD) and I never got anywhere with my GP. Paid to go private in the end. But I'd already gotten a lot of information online so the diagnosis wasn't much use.
For one, the OP has painted her child as a 'loner', yet she has friends! From her childhood, in uni.
Currently , in a dead-end town with few prospects, where does she think her DD, an intellectual, well-travelled young woman is magically going to find friends on her level? I may sound snobbish but it's true.
Secondly, job hunting with a degree like that is overwhelming. There are so many options. Applications for the big grad schemes involve multiple stages, only the last few with a human. Stories of others' success is everywhere, there's a lot of messaging especially in an RG uni that if you haven't gotten a plum grad job after graduation you've failed.
Also, rents are sky high, you can't just 'move to the big city' to seek your fortune as people used to!
It's no wonder she's somewhat demotivated.
OP, I recruit graduates and have quite a few from RG unis (yes, even Oxford and Cambridge) coming in 2 years after graduation.
You can read up about autistic traits, maybe see if some of them like high levels of anxiety, pathological demand avoidance (PDA) applies to her, find some strategies that might suit her. I wouldn't be fixating on a diagnosis. A lot of people on MN are ND themselves and do a lot of projecting. Get the ball rolling if you want but I doubt that it'll be a lot of help.
In the meantime, I think you might have to start charging her a bit of rent, also share some stories etc of people who have taken a year or two to find a grad job.
Is there maybe some volunteering or something else she can do even online, for charities etc that will help her see where her skills can take her.
BTW people who are good at exams can often fall into a rut as it's all they've ever known. Getting good grades is very different to working, in the real world. Its understandable that she's a bit scared. Maybe of failure? If she never tries, she never has to fail. Has she even failed an exam in her life?