I always thought kids could start showing signs of magic at any time. Doesn't it say in the Philosopher's Stone that odd things had always seemed to happen around Harry? And if he could, at the age of one, use a toy broomstick, I would assume that to mean that he already had some visible magic in him. Neville first showed signs of magic when he was 8 (the time he bounced), and that was apparently late. (Quote can be found on this page)