My daughter's teacher will take four year olds, but as others have said, it depends on the individual child and teachers. I'd start by trying to see what teachers you have locally, see what they say. You don't say where you are but you can get lists of harp teachers from http://www.pilgrimharps.co.uk/teachers.htm
The people at Pilgrim are always extremely helpful. I don't know the people at Affairs of the Harp, but I have heard good things of them from others.