Legal Question in Civil Litigation in Virginia

Re: my neighbor kicked my dog

Whose property was the dog on when the kick occurred? Was the dog injured (or didn't you take the dog to a Vet to be checked)?

I assume your question is whether you have a cause of action, and that depends on the facts and the law of the state in which the event occurred. Having a cause of action (or alternatively, "standing" to sue someone) requires two things: a theory of liability and a theory of damages. In this kind of case, your theory of liability would come under some classification such as trespass, trespass to chattels (i.e., injury or unjust retention of tangible personal property), or some special state law defined action. Most actions require proof of "actual" damages: some tangible loss that can be equated to money, such as the vet's bill for the checkup. If there was no harm done, then you have no cause of action, however offensive the behavior that made you think about a lawsuit.

Btw, is there a criminal penalty for cruelty to animals where you live? Check with your local animal control officers.

My advice would be, keep your dog away from that neighbor.