Bath, DD's school isn't in my area but I called them and explained that her needs weren't being met academically at the one she was at. Showed them her report (which was good, not AWESOME or gifted) and they accepted her.
I did wait until the end of year 10 because lots of students tend to leave or do VET type subjects.

I think it's your perception that a public school either can't be any good, or needs to be 'selective' to be of any value. And in the real world it's only the minority that are gifted...