To get back to the original question of the thread, with Therapy Dogs International, there is a rule that any handler under 16 must be accompanied by an adult on a visit. Anyone under that age, who can pass the test with the dog, is able to be certified as the handler, they just can't go on visits alone.

While it might be too extreme, I don't see it as being a bad rule of thumb for most dogs walks. Of course, it depends on the dog and the child, but I think an adult should be in close proximity, for kids under 16, and on the walk with kids under 10 or 12. And is most cases, I don't think kids under 10 should be holding on to a dog's leash alone near roads or in other public places. Of course there are exceptions to everyone, but those seem like reasonable guidelines to me.