If you can eliminate the cause of the bullying, then why not?
Because the cause of the bullying is the people who bully, not anything the person being bullied does. Saying "oh she's being bullied because she has hairy eyebrows" is only one step away from saying "oh she was raped because she was wearing a short skirt". The only thing that will eliminate the bullying is to stop the bullies.
The responsibility lies with the bully not to bully, or the rapist not to rape.
In many cases the "thing" a child is being bullied about is simply a way to get at the child. If she does something about it, chances are the bullies will comment on that too. It won't be the right way, it'll be waxed not threaded, too much, not enough, not HD. They might tease about being so hairy she needed her brows done in the first place, or simply move on to her legs, or the shape of her skirt, or her shoes. Not being bullied is more about not letting them affect you, rather than changing to gain their approval.
If this were happening in our school, the head would have a whole school assembly and address the bullying. There's not much to speak of in our school because the head has all the children understanding bullying- if anyone tries to pick on a child, a bunch of others will recognise it as bullying and remove the child from the situation. When nobody will tolerate anyone being mean or personal about another child, it can't happen. The school should be dealing with the o/p's problem, not just a beautician.