The keeping, housing, raising, use or care of animals is permitted and subject to the following limitations and conditions:
(A) Customary household pets may be kept on a non-commercial basis provided that the number of such animals does not exceed six and that it does not exceed three dogs. This does not include the temporary keeping of newborn animals for a period of time not-to-exceed six months. Customary household pets include such animals as dogs, cats, rabbits, birds, and similar animals; but do not include pigeons, chickens, ducks, geese, goats, sheep, pigs, and other farm livestock.