From what I can tell that's pretty rare. Stuttering hasn't been studied a lot, but for most stutterers it starts basically as soon as they start speaking or a little after. It's called developmental stuttering, and it's the most common kind. In fact, experts recommend to try and catch it and treat earlier because treating it before the age of 7 or so has a high chance of success. Generally they tell parents to wait a bit, because a lot of children speak with disfluency when they learn to talk and they end up growing out of it, but after age 5, 6, or so they should speak with a professional.