Having access to a dog is a luxury. If she is not going to be gentle then she should have her dog time privellages taken. Our 2 yr old is usually pretty good but occasionally he is rough with our dog (who is a lot bigger but a real sook). Often he is looking for our reaction when he stands on his foot etc. When that happens DS goes straight into his bedroom. I am not a big believer in time out but I also have responsibilities to keep my dog safe so will do it in these situations. I then explain why he is in there. I make him stay there while I check my dog to 'see if he needs to go to a dr' (if he has been really rough) and then when he is allowed out he is not allowed to go near our dog for a while. He does love our dog but it is a stage, and you are right in being worried that your dog may eventually react by biting. All animals have their point that they will tolerate.
If you really can't stop her then the dog needs to be able to go somewhere that your DD is not allowed. That way he can control how much time he spends with her and be able to retreat to get away rather than having to resort to biting. You don't mention your daughters age but perhaps she is just too young to understand that she is hurting the dog?