I would imagine it's more the parents encouragement in regards to why she's on AGT. I do agree though that the majority of the reception she had there will be because she's so young, I'm willing to bet half the people giving her applause can't stand that style of music but did so because she's that old. It will however pick up attention for her, she'll likely get something out of it and then fall off the face of the earth in her teen years once the thing that made her unique has faded. Child 'prodigy' or other such terms are always a bit odd to me, for one it's easier to learn as a child (I really wish I'd kept up with music when I was a kid >.<) and for another some people just pick things up quicker - regardless of what age. Any of these things, be it an instrument or otherwise (I've seen "Child prodigy" gamers before ¬.¬ .. woo?) are mostly just going to be the result of being introduced very young and it only being seen as anything different due to the age, which ultimately means nothing.
On a slightly different but related note, I'm not a huge fan of fame for things like that... some sort of, I suppose gimmick. An instance that bugs me is 'The Iron Maidens' the all female Maiden cover band. They have released albums, but the only thing to make them any different to the existing Maiden albums is they are female.... they're no different to any other cover/tribute band, except they're all female (which still isn't THAT uncommon).
Err. apologies, failed to sleep tonight so I'm a bit cranky(er than normal).