The most popular animal images you can use in a pet supplies store logo are of common pet animals: dogs, hamsters, parrots and cat images etc. Since pet supplies are required by people who own pets or vets, you are better suited to use a popular, recognizable image as your pet supplies logo design.
A pet store logo can use an image as is, or add variation in the form of shield logo, key, fish bowl, dog dish, or a location pin logo if your pet store is located in a popular location. Puppy paw prints is another image that's really popular with pet clubs and pet shop owners.