I don't have kids but I will offer this. Bow hunting is all about keeping your shots to within your capable range and determining what is a good shot angle and what isn't. Only you can make the call as to wether he knows what a good shot angle is with a bow. Another question is has he practiced with his bow long enough? Is he a good shot?
Age is not enough to make a determination because I know plenty of grownups who don't practice like they should and can't make an ethical shot on a deer with a bow.