You don't have to give them your insurance information, however, they will be able to get it if they file a lawsuit against you, which they might do.  If you are liable for the child's injury, your insurance company should handle this for you.  If you are not, your insurance company should provide you with a lawyer who will defend the claim against you.  You can either contact your insurance company yourself and make them aware of the incident or you can refuse to provide the information and see where the injured child's parent's take it.