If you give notice now would you only have to pay up to half term in October? Is is a terms notice.?
As question have looked around the local schools for a place for your DD in September? It would be advisable to do that and at least have that up your sleeve.
Its so difficult and we worry about our kids. Only you can know what is right to do for your daughter.
I moved my DD mid term (nearly 2 years ago now) out of a private school as she was so unhappy. They ended up not billing me the extra half a terms fees. I did loose half a terms fees though. However she is very happy in her current school which although also private is much cheaper, so we are happy too.
Have a look at the contract you will have signed when your DC started at the school. It will naturally say that you have to give a terms notice. However also look at what it promised to do for you and see if they have broken their side of the agreement/contract. If other parents are unhappy it might be worth doing this together Other wise you will be stuck until Christmas. You could pay the fees and go to another state school. I know this sounds an expensive option but at least your DD would be learning at the new school.
I moved my eldest dd from one when she was much younger, I was very unhappy with the school and found out that they had lied about something very important to me.
I argued with them for over a year, but they did end up taking me to court as the contract was a terms notice. They tried claiming for costs plus interest which they weren't awarded so I felt the judge had some sympathy with me.
It depends whether the school is part of a big group ( mine was gdst) , how much support/evidence you have etc.
I don't regret doing it as dd had to move anyway and I was so angry with the school that I was glad to have caused them a small amount of trouble.