First, I would like to say I am so sorry your dog was hurt. I hope the news at the vet is good. It is a terrible thing when they are hurt and you are waiting to get to a vet to find out the extent.
If you watch this child, I am sure you have cautioned him many times about being gentle with the dog etc. He needs a serious talking to about the consequences of his actions and find out WHY he did such a thing. The parents, if they are decent people, should offer to pay for the vet expenses. There is no valid reason for this child's behavior, at any age. Back in the day (I am showing my age) we never dreamed of doing some of the things you hear kids doing today.
Don't beat yourself up, you had no idea this child was going to do something crazy. I have a strict rule, my two grandchildren know they are never allowed to pick up the dogs. They would never intentionally hurt them but too many things can happen. It is so easy to drop them, I worry about adults sometimes. Just when I think I may overreact, I read your stories such as yours.