A person who shoots a dog is damaging the property of the dog’s owner and can be charged with the offence of criminal damage. A conviction could lead to a fine, imprisonment, a compensation order and the revocation of the shotgun certificate and/or firearms certificate of the offender. The moral, therefore, is only to shoot a dog as a last resort.
That said, the owner of livestock, which includes domestic poultry such as yours, has a defence at law to a civil claim for shooting a marauding dog, providing the shooting is really for the protection of the livestock and the police are notified within 48 hours. Also, it is a defence to a criminal damage charge to show you had reasonable excuse, which would apply in your case.
At law, then, you can shoot marauding dogs without being convicted of criminal damage or being sued for damages. Be warned, however: you are likely to stir up such a hornets’ nest that you will wish you had never seen the wretched dogs in the first place, let alone killed them.