The board may provide for the prevention of injuries to sheep by dogs, and for the destruction and control of predatory animals, and may tax the possessors of dogs and direct the application of the tax. The board may, by ordinance, require veterinarians licensed pursuant to Chapter 11 (commencing with Section 4800) of Division 2 of the Business and Professions Code to report to the county the shooting or poisoning of any dog. Such veterinarian may be required to report the name of the owner of such dog, if known, or the person or persons requesting treatment of such dog.