Clearly, this child is insane. Eleven year old children don't go around murdering people if they are sane. Additionally, this child must have exhibited some symptoms of mental illness prior to this. It's begs the question, why weren't they caught before this tragedy?
As much as people don't like to admit, sometime people with debilitating psychological problems do commit unspeakable, violent crimes. They need to be treated, especially when they're children. If they are "untreatable", then they need to be medicated and placed in a secure facility, to protect themselves and the public. But, they don't need to be placed in prison with life-long, violent offenders.
Let's assume you are right. Why wouldn't prison be a good place to keep them...if they're insane they probably wouldn't even mind.