Good on your DD - it's great to encourage her to aim high and she sounds really mature and capable.
There are lots of things that you can do even this far in advance to boost her chances.
Oxbridge colleges look for evidence that a young person can manage a complex workload in a self-motivated way - extra-curricular activities and volunteering can help demonstrate this. In Y7 she won't be ready for this just yet but by the time she is 16/17 she should be capable of investigating and self-teaching additional subjects outside her ordinary studies for the sheer love of learning. Oxbridge expect their students to be extremely self-driven to learn - the do not get spoonfed facts but are expected to research and find out for themselves and then develop original and interesting opinions (arts) or testable theories (sciences) based on what they have read.
She also needs to be well-rounded and able to contribute to college life so encourage her to develop skills in sports, arts, debate/public speaking etc. She should have some skills across a wide range of extra-curricular activities, and should pursue one extra-curricular thing to an advanced level sufficient that by the time she is 16/17 she is winning prizes/awards/regional recognition for that thing, so that she can stand out and shine - her application, when it eventually is submitted, will be just one sheet of paper among hundreds of others each of which is from very bright, very talented young people who love science and want to be a doctor. When there are way more talented applicants than there are spaces, getting noticed is partially luck and partially having just something that makes you stick in the mind and seem slightly different from all the others.
She absolutely should go for it, and give it every ounce of strength - as you have already said, it's even harder to get in if you don't try - and everything she does to try will also stand her in good stead for getting a good place somewhere else if she isn't one of the final few to be selected.
Do also look into USA ivy-league universities - the richer ones that have a needs-blind admissions policy can end up being cheaper to attend than UK Universities if she ends up qualifying for a partial scholarship. They will have even more stringent needs for being talented in extra-curricular things and the competition is just as fierce if not more so, but it might be worth a look.