Why do you want to send your daughter to that school?
Because it is private? That in itself will only be an advantage if she wants a job where snob value matters.
Because it will support her music? That could be a big issue. DS played the cello at state primary school, but only because I kicked and screamed and made them give him the opportunity (I had to drive him to another nearby school for the lesson and then back for the start of lessons, he missed registration and assembly). When he started at a private school and said "I want to learn the bassoon", they said "cool, we don't have any bassoonists right now, we'll arrange a teacher and instrument."
Academic standards? That will depend on the school. Being private certainly isn't a guarantee, and I'd never suggest sending a non-academic DC to a school - private or state - which is obsessed with league tables.
Sporting opportunities? DD's school were great about her missing time to compete at a high level in a non school sport. Several of her friends at state schools would have mum finding a quiet corner at the competition to ring up and lie about their DCs being ill because they wouldn't authorise that sort of absence. Not sure what the current state school rules say.
To be honest, though, I think the best start for your child is for them to go to a school which suits them. I don't think you can make a general statement about that always being private or state any more than I think you can make a general statement about it always being large or small, or single sex or mixed, or 11-16 or 11-18.