We moved our 9yo DD a couple of years ago.
She didn't want to move AT ALL initially. She was horrified by the idea. She then went on several taster days at the new school where she was made very welcome (she was moved from state to private, so this was easy to arrange; not sure what it's like if the new school is a state one).
Eventually she came round to the idea a bit more and was torn between moving and staying. We basically then told her that the new school would be better for her and she was going to move there in the autumn after finishing the summer term in her old school.
It was hard to strike a balance between listening to her feelings and acting in her best interests. So I feel for your position. After a while we just needed to tell her what would happen so that she would have some clarity. But by that point she was less reluctant anyway.
After a week in her new school she spontaneously told me how glad she was that she had moved. She is very happy there still.
One v important thing to bear in mind... Kids normally really HATE the idea of moving school. We did some research on this at the time. The only real exceptions are when they are being bullied very badly or have some other serious issue. Otherwise they tend to feel great loyalty to their school, their classmates and their teacher. Even when the school is a bit crap, it's their territory and they are familiar with it. In fact it may be the only school they've ever known.
You will get a more positive response if you can get them to go on taster days, or otherwise build their familiarity with their new school. Otherwise you are just asking them to make a leap into the unknown.
In the end, after a certain amount of discussion and familiarisation, you may just have to tell her that it's going to happen. I would listen to her views but I would not let her have a veto on this.