I like Herons and have rescued them and would hate to see one killed,
but accidents can happen. I'm just wondering what the authorities feel
about the natural instincts of certain breeds of dogs?
snip

I suspect you'd be in no trouble at all. Your dog in your yard? Hardly a
crime. Now, if you shot the bird and held it down for spot to kill, that
might be an issue.

I'd imagine that you are legally responsible for everything your dog does.

I think the penalty might be different between dog kill and gun kill
but both would be guilty.