I am not aware of any age limits, but here's why I don't think it could actually happen. Only 19 people have ever qualified for grandmaster before the age of 15, and there's a big difference between being "just" a grandmaster and being good enough to be invited to the candidate's tournament - right now there are over 1300 grandmasters in the world.
Winning the junior world chess title does NOT qualify you to be in the candidate's tournament. The candidates for the 2012 tournament are as follows:
Loser of the World Chess Championship 2010 match
Loser of the 2009 Challenger Match
Winner of the FIDE Grand Prix 2008–2010
Runner-up of the FIDE Grand Prix 2008–2010
Winner of the Chess World Cup 2009
The next 2 highest rated players in the world
Tournament organisers' nominee (must have Elo rating over 2700)
The winner of that will play the current champion.
From that, you can see how difficult it would be to actually win the championship at 15. At 15, you wouldn't have been in the previous championship or challenger match, so those 2 ways are out. The Grand Prix started in 2008 and the World Cup was in 2009, so if you would be 15 in 2012, you would have been 11 or 12 in those years - even if someone became a grandmaster that young, would they really be good enough to get invited to those events? The next way to qualify is to have one of the 2 top ratings in the world. For someone so young, I doubt the rating would have caught up to their true ability, even if they WERE that good. You have to play a lot of games for your rating to go up that much, and the ratings used are the average of the 2009 and 2010 ratings - so again, you'd be 12 or 13 at that time, to be able to win at 15. And the last slot is given to someone from Azerbaijan, where the tournament organizers are from (and again, the person has to have a rating over 2700, which is unlikely for someone so young even if they were good enough.)
And even if you somehow qualified for the tournament, you'd still have to win it... and then win against the current world champion. So, although there is no specific rule against it, I doubt it would ever happen.