For a school system to punish a kid for defending themselves is unthinkable yet I know that a lot of boneheaded, stupid idiots in school administration have the idiotic idea that in any fight, both parties are to blame. My Father was in school administration and this subject would get him fired up fast. He would go against the other officials loudly to say that many times a fight only has one guilty student involved and the other is simply getting picked on. I fail to see how any adult who has lived through school themselves can think walking away from a bully will fix the problem. They'll keep doing it until they are physically stopped and the kid who hits back should not have to suffer ANY consequences.
I do know of one teacher who had a kid that was getting picked on in his class. This was a shop class and one day the kid who had been picked on finally had enough. He got a 5 gallon bucket and filled it with hot water. Then slipped up behind the bully and poured it all over him. The teacher turned his back when he saw it happening and just laughed silently to himself. A lot of teachers would have jumped on the good kid but this teacher had enough common sense to recognize justice when he saw it. The bullying stopped too.
I hope yor Daughter beats the crap out of the bully girl myself.