I think you are on the right track. Self defense sounds good, kickboxing maybe? I work in a school and know that it is strict policy to tell all kids in our school that if they engage in fighting in any form, whether it's self defense or not, they will be suspended. They expect them to come to a teacher or administrator for help as the solution. My boys have had small incidents with other students that had prompted me to tell them that if someone messes with them to punch them in the nose because the laws of nature state that basically, bullies pick on someone they perceive to be weakER than them, so if they are not put in their place they will continue. If a kid goes to teacher or administrator about someone messing with them, then the bully will think it's funny and keep on. They will seek revenge at a later date if they get in trouble. It's pretty crummy but the system for dealing with a bully if you are the one being bullied doesn't work too well. Kind of have to take matters into own hands, literally.
All the best.

Thanks so much for your response. The teacher actually called us over the weekend, so maybe they are taking things a bit more seriously. I will keep a close eye on the situation.

My daughter started Judo lessons last week. Right now, she is thoroughly enjoying it. I am hearing that it can help boost confidence, and help with physical fitness, so it's not just self defense.