[astura]

No, Depending on the specifics you probably will be charged criminally - the statues you would be charged with will vary by jurisdiction but discharging a weapon into your neighbor's yard is, largely, very much illegal. So is intentionally harming other people's pets - even if it's legally classified only as intentionally destroying someone else's property. Animal cruelty charges might also be a possibility depending on the specifics.

You'd likely also lose a lawsuit if the owner sued you for vet bills incurred trying to save the dogs life.