To be perfectly blunt, I don't really believe in the idea of punishing criminals. I think that a better system is to attempt rehabilitation. Unfortunately in this case, the girl is obviously a sociopath, and there is no cure for sociopathy. I think she should be locked up forever, not so much for this one act, as for the fact that if she's a sociopath it's not unreasonable to think that she'll do sociopathic things in the future. Since there is no way to rehabilitate her, the only choices are either to lock her up for life, execute her, or somehow keep her under 24 hour surveillance for the rest of her life. Of those three options, I'm inclined to think that the first would be the best.
However, we live in the real world, where we don't rehabilitate criminals, we do just punish them. I don't feel like I really can comment on whether or not that's an appropriate punishment, since I don't think a punishment is the right way to go in the first place.