Bullying culture is a bit like rape culture, isn’t it? We are far more focused on raising girls to avoid being raped than on raising boys not to rape. The argument that your daughter should shave to avoid bullying follows pretty much the same flawed logic. Maybe we shouldn’t expect girls to conform to arbitrary standards to avoid bullying but spend that energy instead on helping kids to recognize bullying and stop doing it.
At some future point your daughter almost certainly will shave to conform. But at yet an even more distant future point she’ll remember her mother telling (and modeling) that it’s perfectly fine to not shave. At that point, she will be in a position to truly make a personal choice — and that’s a gift only a conscientious parent can give her child. Well done.