Well my two cents. Calm down. In the grand scheme of things this is really no big deal. I don't see this as a RKBA issue, unless you're gonna either hunt it down and shoot it (illegal) or wait for it to come back and shoot it (likely invalid self defense)... also - issues with discharging a firearm in a urban area to consider.
Are you sure the your son didnt provoke the dog to bite? Not unusual for a toddlers to provoke even the nicest dogs into biting to defend themselves.
Pulling a dog's ear or sticking their fingers in the dogs eye etc
Bingo
In a year you'll have forgotten about it. You have no proof that your kid didn't provoke the nipping, a nipping is no big deal (equivalent to a cat scratching), and rabies is practically extint. All the owner has to do is show evidence of a current rabies certificate/vaccine. 10 - day quarantine if you're really worried about it.
However if you go blasting a neighbors dog, or create an irreversible rift by getting a neighbors dog put down for an accident... it could end badly for you. Let's just say that these "trivial" neighborhood skirmishes can quickly escalate into macho <
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As a dog owner, sometimes dogs get free. And they can nip sometimes, espeically in self defense. Heck, I watched my neighbors dog nip at a kid just this weekend. Kid cried for a minute and then went on playing. Dog was spanked, end of story. Dogs that nip are different than dogs that attack or maul.
If my neighbor killed or had destroyed my dog over something trivial like this there would be consequences.
Ensure kids medical needs met. BTW - rabies is practically non-existant in the US in domesticated pets. If the kid has medical bills, talk to the homeowner about paying for them.