I've been following prodigy drummer kids on youtube for years now, some are crap, some are pretty decent. My son fell into the latter category by the time he was 4. He started drumming on my kit when he was 2 and it just clicked for him. He used to pull in audiences at Guitar Center. His sister wanted to go to Chuck E. Cheese, my son wanted to go to Guitar Center to play drums (though he couldn't reach the bass pedals with their stools). Unfortunately he decided for a few years he was no longer interested, so while he's getting back into drums now, he could have been much further along than he is. He's still FAR better than most 7 year olds, but I wouldn't consider him in the prodigy territory anymore.
We tried to get him into the music program at his school last year when he first started but were told he was too young for drums. We asked the music teacher just to listen to him, but nope, too busy. This summer the school offered lessons so we signed him up simply so he'd have the opportunity to be heard. For the first 3 weeks the teacher just had him doing REALLY basic stuff, so of course my son grew bored. We finally said to the guy have you just asked him to play for you? No? Next week, please just ask him to play. We returned to pick him up and the music teacher was completely blown away and said he was playing better than most of his 8th graders and we should be sending him to a drum teacher rather than relying on him as a generalist (but teachers around here charge $75+ /hr). By the last lesson they were jamming together which my son had never done with a live person before. Needless to say, he'll be accepted to the drum program this coming year. He was invited to jam with Gary Hoey during his sound check but chickened out. That would have been pretty cool.
In the end though, I'm not one to push my children to do stuff they don't want to do. If he wants to be a drummer, great, but he loves keyboards too, so whatever makes him happy.