I agree with all of the above.
I think your key to find is the top distance safe for their age.
i.e. you wouldn't go toss a 12 yo in a full marathon even if they could do it. It simply isn't safe for their bodies (and hence why marathons have age minimums!)
I don't know the structure, but the more knowledge you have, the better you will be able to keep your child safe to make sure they are not overtraining for their age and physiology.
If you got to a running specialty store, they are often staffed by folks who actually run who may be able to give you some advice as well. They might also know of some good books as well.
I remember at 9yo, I was doing some 2-3 mile runs with minimal training. While I don't recommend that (I was told when coming off of the plane for a visit that my dad had put me in these things.

), I'm just mentioning that with training, those distances are not too bad.
Also--some people are built for sprint distances while others are built for endurance. I'm built for the latter. I run like a snail, but can go very far with adequate training.
Injury prevention is also key. Being familiar with what are "normal" aches and pains of training for a sport versus what is an injury and being comfortable resting an injury. Avid runners often get antsy when having to sit out for a seemingly simple but painful injury. But not doing so could sometimes mean never running again.
I would also check the coach's experience. What training they have had, what they have run, and what their overall philosophy is.