There's no rush to decide at 13, but also no harm in starting to gather information. There will also be open days to attend nearer the time.
Maybe send off for some prospectuses from a variety of different universities (or read them online)? I remember looking through them for the first time, and it was very helpful to see how the courses differ, what the places look like, and all the courses I'd never heard of (i.e. anything that wasn't a school subject!)
DD can read around her favourite subjects in addition to the material learned at school. When the time comes, this will demonstrate a genuine interest and self-motivation to an interviewer.
Perhaps also think about any particular combinations or specialisms which are available. Again, not in order to decide yet, but just to know something of the wide range of courses out there. (I certainly didn't have the first clue about any of that at 13!)
Just for example, some of the courses at Oxford include:
Classical Archaeology and Ancient History
History and Economics
History and Modern Languages
Fine Art
Archaeology and Anthropology
Oxford and Cambridge don't offer every degree or every option for everyone, and your DD will have several more spaces on the application form, so find out about as many places as you can. She might decide that the Graphic Design course at the Manchester School of Art is right up her street, or Ancient, Medieval & Modern History at Durham, or History and International Relations at Exeter.
It could also be worth looking through a careers website such as Prospects, as they have pages on the jobs you might do with a particular degree, and statistics on where graduates in each subjects go next.
E.g on this page www.prospects.ac.uk/careers-advice/what-can-i-do-with-my-degree/fine-art it says a sixth of fine art graduates working in the UK are employed as artists.
Sounds like your DD has a supportive and enthusastic Mum 