Since you're asking, you must have some nagging suspicion that a handshake deal might not be good enough. If so, you may memorialize your agreement with something in writing. People in your position sometimes will ask a seller to represent in writing and/or prove to you that he has title to the dog and authority to convey it. They may ask that the seller agree to indemnify them against any future claims from alleged owners or co-owners. You could have a discussion with a qualified NJ attorney to prepare an appropriate document.