It's really tricky to change schools mid-way through their GCSEs as there's no guarantee that other schools will be doing the same exam board for all of her subjects, so she may have an awful lot to catch up on (depending on when you'd move her).
I have a DD in Yr 10 too, she had a close group of friends since Yr 7 - they were all boys and she seemed to get on really well with them, they included her in meet ups outside of school etc. Mid-way through Yr 9, she started to find them incredibly annoying - they were just being 13/14 year old boys, but the toilet humour and un-PC "jokes" got a bit too much for her and she decided to back away. She felt she had no friends at school and was very unhappy for a while.
In the meantime, she had come out to us as being gay, so we found an LGBTQ+ youth club, which she now goes to. She made tons of new friends there - even a couple who are at her school. It meant that with these new connections, she was able to find a new group of friends who seem like a brilliant bunch! DD has also started at a local drama group where she has made more friends, who she tends to make plans with to see at weekends etc.
I do think that your DD needs to push herself a little here - I know it can be uncomfortable to approach new people, but until you try, you just don't know - they could be her lifelong BFF! My DD is forever going up to people in town and saying "Hi, I really like your style/hair/make up, can I get your Instagram as I'd love to follow you?", which has resulted in several more new friends, but does take some confidence to pull off (I don't think I could have done it at 14/15!)