I’d suggest you start by drawing up a list of schools which are within a reasonable journey as a starting point. Decide whether you’re going to confine yourselves to all-girls options and within that whether you’re going to limit choices to GDST (the latter restriction would be an unusually narrow target at 11+, but obviously it’s up to you).
Don’t underestimate the burden of an onerous commute. What may sound doable in theory quickly becomes a real bore on a cold dark winter’s morning when they’re carrying an instrument or an art portfolio or sports equipment. Once they get to about Y9 and the homework level ramps up, life will be much easier for a teen with a straightforward journey to and from school. It also enables them to take full advantage of extracurriculars, without becoming too tired.
In the autumn term, start visiting the schools on your list. Your gut feel will tell you a lot about where you see your DD thriving.
Tutoring: What can be helpful at exactly this time (late Y4/early Y5) is an assessment with an experienced local tutor who knows the target schools and can tell you where she’s at compared to the level required for those schools. We are in north London, so a different set of schools, but we did find this helpful coming from state primary. If she’s currently in a private prep, the Head should be able to guide you on whch schools to target.
Mine are thriving in selective indies without our ever having paid for tutoring beyond that one-off assessment. However, I did do structured work with them at home using sample papers available online and also CGP books to cover those bits of the curriculum which hadn’t been covered at school. Maths in particular needed a boost (but that may just have been because it was a particular weakness at their primary). You’ll find many people saying they never tutor, but in reality many of them will be educated parents doing what is effectively DIY tutoring. As with everything in life, those who turn up to the exam with some preparation in the tank will have the best shot at showing what they are capable of.
Be aware that there is now a Private School board on here where in theory you (and I) are less likely to be slammed for choosing the independent sector. You may be able to get more specific feedback there on your options, and perhaps especially to pinpoint those which will get the best out of bright children with neurodivergence.