Each person who owns or keeps a dog, cat, or ferret that is 4 months old or older shall have the dog, cat, or ferret vaccinated adequately against rabies. A county may not register or license a dog, cat, or ferret unless the person who owns or keeps the dog, cat, or ferret submits, with the application for registration or license, proof that the dog, cat, or ferret has been vaccinated adequately against rabies. The public health veterinarian shall determine the proof of vaccination that is acceptable.