Have you asked the LA whether there are schools which definitely have a place in the relevant year group?
Caveat, 1. where all schools are academies / foundation / VA, the LA will probably direct you to ask the individual school and 2. since even if there is a place available when you enquire, and no-one on the waiting list, the only way to get a place is by submitting a formal application, and by the time you do, someone whose DC ranks above yours against the oversubscription criteria may also have applied.
If you apply and are turned down, you have the right of appeal, but this takes time and success depends on the relative merits of the schools case not to admit another pupil into the year group, versus your expressed need for a place there,
Depending on how you are placed to pay for a place in an independent school (assuming one is available locally), or to home educate, an 'outstanding' school for your DD may be the one which is logistically possible and has a place available.
(I'm afraid that doesn't help you much with the 'which schools are the most desirable?' question, but so many responses to this sort of question on MN concentrate solely on the 'best school' aspect and ignore completely the fact that there actually has to be a place to offer).
Aside from that, you might be better off starting a new thread, with the area in the title.