While the shooter may have the right to discharge a firearm on his property legally, depending on the local laws, the courts would take a very dim view of someone firing a gun when there are children in close proximity. A load of buckshot can travel 50' in a very short time. That alone sounds like careless dicharge of a firearm.
Definitely seek a lawyers advice.
It would be careless or dangerous use of a firearm only if it was pointed at the kid or if the kid was in any sort of danger of being hit by stray pellets. The OP does not say where the kid was in relation to the gun, the dog, and the line of fire. Simply being "close" is not sufficient to lay charges. Psychological "harm" is also not sufficient unless the psychological harm comes as a direct result of having a gun aimed at or shot towards the kid.
The reason I asked what kind of dog is to find what possible avenues of defence might be open to the shooter. Even if the shooter doesn't have livestock or poultry, he can still fall back on a claim of defending himself against what he thought was a dog was about to attack him. Shooting a poodle because of claimed fear to life and limb wouldn't go far, but a Rottie is another story, especially at night. It all depends on how the shooter describes the incident to the police, and whether the police believe the story to be credible or not.