It really sounds as though the problem is the friendship group, rather than the school. That doesn’t mean that moving schools is necessarily the wrong thing to do, but it’s worth seeing if you can help your DD to move on from this group first.
When a friend’s DD went to secondary, she found herself in a group with popular, trendy girls that really weren’t her people, but she lacked the confidence to make new friends. She has struggled all the way through (she has just done her GCSEs), tagging along with this group. She didn’t have the confidence to move schools and break into established friendship groups, but they did consider her going to a ‘business’ school which starts in Y9 so she could have another go at making friends when everyone was new together. However, the GCSE options were limited, and she could have made the same mistake again. She is going to a 6th form college rather than a school 6th form, in the hope that once again everyone will be new and she can get lucky. The issue is really that she is so shy that making friends is very difficult for her.
When my DD started secondary, she made friends with a couple of other girls who were not troublemakers, but just not really her people. She struggled a bit during the first year and, knowing that the teaching groups would be mixed up again for Y8, towards the end of Y7 she asked not to be kept in the same group as these girls. This forced her to make new friends in Y8, and it was better, but it wasn’t until Y9 that she really found her tribe.
The difference with my DD is that she recognised that she wasn’t with the right friends, and she did something about it – twice. It did mean being a bit lonely for a couple of weeks (at one point she was actively hiding from her old friends to break the habit!) but it worked.
Luckily for DD, her old friends didn’t make life difficult for her – everyone simply moved on. If your DD’s current friends are a bit popular/dominant, it might be hard for her to move on from them, even if she wanted to.
Perhaps you could chat to your daughter about these friends and how she really feels when she is with them, and if she thinks they are her people. It sounds like the school would be supportive if she did want to separate from them.