The whole thing is just sad. Whatever happens to this girl, her life is over either way. Even if she were to become completely rehabilitated, she'd have to live with the guilt and the judgment of others. Like someone else mentioned, no one will want to associate with a child killer. This would, most likely, drive her even more crazy. It's not gonna end well.
I do believe that she probably has a mental disorder. The article said she had depression, and to the guy who said depressed people only kill themselves, not others, is wrong. Clinical depression isn't just "feeling sad". It's kinda hard to explain it to those who haven't felt that bad before, but full blown despair is good starting point. How it affects people also varies. Me, I just cried and slept a lot. Some hurt themselves. Some go crazy. People with depression often have or acquire other disorders along with it.
I'm not saying it's an excuse, just something that needs to be taken into consideration. As was pointed out, the article mentioned that the girl dug two graves, but she only killed one person. After finding out "what it felt like", it's likely that she was going to put herself in the other grave, or at least had the notion of it. Maybe she thought she wouldn't be able to live with herself afterward, maybe she thought it would make up for it, or maybe she wanted to kill herself all along and decided, "what the hell, might as well take someone with me, see what that's like, since I'm going to be dead anyway." Clearly, she is not mentally stable.
As to what should be done with her, it's tricky. Personally, I think she should kept in an asylum for a long time, if not the rest of her life. It's not a perfect solution, but in this case, I don't think there is one. I don't see her surviving in jail, nor do I see her recovering and becoming a functioning member of society. Maybe if she had gotten some kind of help earlier on, if someone had only realized what she was thinking, things might have been different. But when you take another human being's life, especially in a situation like this, it's not something you and/or others can get over. It's permanent.