HEAVENER, Okla.—Bernadine Himes leans over her nursery—a row of blue laundry baskets, lined with heating pads—and picks up a squirmy, week-old English bulldog. The puppy, half-bald and no bigger than a hamster, nuzzles into her cupped hands.

Ms. Himes and her husband, Terry, have been breeding dogs for decades on their ranch here in the wooded hills of southeast Oklahoma. They sell at least 150 pups a year—at an average price now of about $800 apiece—to brokers who place them...