Two things come to mind here:
1) According to the article in the OP, the 11-year-old girl is from a Christian family. How did a Qur'an come in her possession in the first place?
2) Assuming that the Qur'an coming in her possession was purely coincidental (and I really don't think it was), why would she think of burning it? People don't usually burn books, let alone ones held to be holy by large groups of people (in this case, the majority of the country).
It seems to me that the girl was despicably manipulated by intolerant people who wanted to spite Muslims in the area by burning the Qur'an. She shouldn't be punished at all; prepubescent children aren't held accountable in Islam for anything they do, so arresting an 11-year-old girl and charging her with blasphemy is simply inhumane.
Of course, that's not to say that Muslims in the area who called for her arrest and punishment aren't a bunch of ignorant, cruel, and uncivilized wastes of oxygen.
Who would have thought a irrational belief in the supernatural would lead to the irrational thought that a 11 year girl should be murdered for burning some paper? Are you still not making the connection?
When you have people calling for the death of a mentally ill 11-year-old, it becomes very apparent that the issue is about far more than "irrational belief in the supernatural." These are cruel, uneducated people; the incident was just an outlet for their barbarism to show.