Ms. Yang, 27, places a hat on her pet Eclectus parrot. Quitting her day job in the media industry, she started a company making and selling costumes for parrots. She sells the outfits online to a growing market of pet owners. The Ecletus parrot is originally found in countries including Australia, the Solomon Islands and New Guinea. Recent new laws in China have made it increasingly difficult for people to own birds as pets. Many species, including parrots, are now deemed illegal.