Do not let your child run scared of bullies.
Changing her hair will not stop them because these predators smell fear. They'll know they've rattled her.
Get your daughter some uplifting reading material that will help her gain a sense of perspective.
'Queen Bees and Wannabes' should help her see what's happening and understand the dynamics, above all, that the problem is the other people's inadequacies and insecurities, not her hair. You and she could read it together.
There is an American Girl Publisher book on peer relationships you could get too - 'Stand Up For Yourself and your Friends'.
Look up the 'Smart Girl's Guide' series of books too, dealing with peer relationships.
On personal appearance, my own red-haired DDs (and their sisters as well) loved the Bobbi Brown book, 'Teenage Beauty'. I think it's still in print. If not, you can find a used copy online. This is a truly excellent book that aims to help teenage girls accept themselves as they are and stop feeling they must change themselves.
Its really important for girls to develop self possession as they go through their teen years. In order to achieve that, they need support and insight into their peers' behaviour and motivations, and also their own feelings about themselves. They also need to develop the connection they have with their parents, especially their mums, as they transform from children into young women, and if you can give your daughter the confidence that you have her back and support her as she develops her own identity, you'll build a foundation for life.