To be honest, I'm afraid I don't think that would be an option but you'll see what school says first thing tomorrow.
If an exam is a module (ie GCSE modules in Year 10 or AS level exams which are considered to be a module of the A'levels) there could be an opportunity for her to take it as part of the January re-sits but if it's a terminal exam then no.
The reason I know what I've posted above is that my DD17 was really, really ill with a virus before an AS level. I was beside myself - it kicked out several days of planned last-minute revision. The day before the exam, I called the school and asked for some guidance - they told me what I've posted above.
As it happened, my DD was fully recovered in time for her exam so we didn't ever get a Doctor's letter or go down any of these routes.
Try to stay calm and act swiftly and decisively tomorrow morning - get on to that GP's appointment and school ASAP!
Sadly, this happens every year to a small percentage of kids. It's disappointing and terrible, unfortunate timing but it's not a disaster on an epic scale. She will not end up on life's scrap heap as a result of this - you'll deal with it in the morning.
In the meantime, the best thing you can do is be calm and confident and kind and reassuring for
Wish you both well and hope it pans out ok...
Good luck.