my first idea when I read this was:
"you have to give her a strong, but not too strong clout and say "when you ever do this again, you get another one", because you´re adult and the older brother and she has to respect you and you can not act so cowardly, because so she not respect you."
I also thought "oh what the hell. 11 years old and already this sick in the head. maybe she has mental problems."
I think it´s the task of parents to raise a child and clout and physical or emotional force is not okay, but you can never ever accept it when someone treats you like that. no matter if little sister or someone else.
and that what she did was not some harmless playing, it was some sort of abuse.
when someone ever would attack me, I would hit so long as necessary to realize my right of self-defense and so long it´s necessary to protect myself (in the borders of the law).
I never walloped someone and I´m glad that this was never necessary, but I would definitely try it, when it would be necessary. I never learned martial arts, but I would maybe try to choke the person, perform hits against the head or the throat/larynx, pressing my fingers in the eyeholes if necessary, breaking the wrist, kicking in the weak spots if necessary. everything which would be necessary to protect myself, but in the borders of the law and not more fore than necessary. in the absolute emergency using tools like knifes or other things which lie around.
but sure it depends if the person wants to kill you or similar or if it´s "just" a pub fight. in a pub fight you can and should use less force. and always better try to escape (if it´s possible).
it would be sure no disadvantage to learn martial arts, but I´m too lazy for that and I don´t like to be touched, even when it is training. but to learn it, you have to train with others I think.
I think the most important would be to not fall into state of shock in such situation, but to fight or run away instead.
I think the advantage of knowing martial arts would be that you could bear down someone, without dealing too much damage to that person and without suffering too much damage on yourself. you could solve a fight "bloodless." or more bloodless.
but this is different than this thread. and a 11 year old is usually no real danger. the best would probably to speak with the parents, but yes, the thread creator was not online for long time, like tree said.