My dog was on my next door neighbor's property, so he shot her, and later that day we had to put her to sleep. While it sounds as if your neighbor was quick on the trigger, it is difficult to know for sure without witnessing this violent event.
People have a right to defend themselves, their families and their livestock from animals.
But unless your dog was posing an immediate threat, there was probably no legal justification for shooting her. This is true even though you may have been violating a leash law by allowing your dog to wander onto your neighbor's property. Your recourse is to sue your neighbor in small claims court. But that may not do much to relieve your anger and sorrow. It will certainly not make you wealthy.