My dog is my constant companion and best friend. To lose her in such a callous manner would make me heartsick. Certainly the person who shot your dog should be prosecuted, if possible. Since he shot your dog so openly, with no attempt to conceal what he did, I suspect he may have the law on his side. But you should certainly find out about that, as I’m sure you will.
Ironically, people have been prosecuted recently for shooting bears that broke in and were in the process of ransacking their houses at Lake Tahoe, as the bears are protected there, but there was a story about a year ago about a rancher who shot two dogs some ladies had taken onto his land. There was no livestock around at the time, and the ladies were just looking for a place in the country to take their dogs for a romp. But a rancher is allowed to shoot any dogs running loose on his property without warning. Other than the newspaper warning people not to do that, there wasn't anything anybody could do about it.