Folks: Mike and I have had these conversations with regards to my own son. At the age of nine, he was shooting Steel matches with his Buckmark .22. In the last few years, Iowa changed its law in such that my son cannot shoot a pistol until 14. Reflecting on that, it was good in a way because it gives my son more time to mature as well as get a more formalized course (hunter's safety) out of the way. We all have that paternal pride, we want to spend time with them in sports that we all enjoy.
On the serious side, Mike is right, a simple distraction or lack in judgement/experience by the child can have very serious consequences. If the hand strength is not there, would they force a bad postion to work out of a jam? I don't think anyone here would say that their kid is that good and they would never have an AD or ND.