As said before by someone (who appears to know) the dog has to be actually attacking the livestock with intent to harm it. as far as I am aware, and I do try to keep up with shooting regs, if the dog is just harassing livestock you can't shoot it. I think the only exception is pregnant sheep as they lose the lambs at the drop of a hat . Either way, I think you would have great difficulty about shooting what is after all a pet.
if anyone know different then tell.
mate all I know for fact is this cnut Will shoot ya dog and not even blink some times we get on his farm with a lamp and no dog