She does need to swap GPs, if she needs regular meds the advice is always switch to the one where you spend the majority of your time. Just because GPs have a boundary/catchment area which you must be in as a patient. Now technically if she doesn't inform them he's going, they'll never know as she can come back home etc but the boundary is typically including prescription limits for what pharmacy's they can send them to.
So if she needs a prescription every month, she'll have to let them know he wants it at x pharmacy and they may refuse to do so, depending on the distance, it's really up to them. But most won't as they already have so many patients in the actual boundary.
It's always better to register at the place where you can then see your GP whenever you need to - she may need medication reviews and have flare ups. I'd definitely change for logistics. Unless she's not going that far, and universities may have walk-in-centers but they often ate just like a minor injuries, not for monitoring a chronic condition or prescribing repeat meds.
Staying with the same hospital/consultant in secondary care makes sense as otherwise you'd have to go on a waiting list for a hospital near her in university. Plus she can come down for the occasional appointments with a consultant. Even if she still lived at home, she could have chosen (when referred) a hospital further out under right to choose, so she doesn't need the GP and consultant to be in the dame trust etc. I'd just let the university Disability team know, and they'll be fine if she has to come back for a day to see her consultant.
Also I'd get her to cancel the appointment with her home GP, if she's moving out before then, as she'll just be wasting an appointment. Maybe try and get it moved up and then get a last prescription of everything for a month, to hold her over till she can male an appointment with the new GP. She can register with the new GP now but just ask them to not process it till x date, so she's still under her home GP. She'll need to do the med review with new GP within the month as most don't prescribe first without an appointment.