There's a distinct difference between combat sports
and actual combat or self-defense. The first adheres to certain rules and conduct, while the second is assumed to be a life or death situation.
In self-defense, the idea is to overwhelm the opposition with violent force by any means necessary. You don't need martial arts lessons to know that the groin, face, and neck are three of the most vulnerable places on the human body, and that a blunt or sharp weapon will throw the odds in your favor quite drastically.
Bullying is not really a self-defense scenario, it's usually just name calling and intimidation. Thus, I don't think it's advisable to train your daughter in possibly lethal fighting techniques for dealing with bullies. If she understands when it's OK to use things like this, i.e. she's actually being assaulted, someone's attempting rape, a violent robbery, or something, then OK. But she's pretty young...