Shabbat: Moving Animals

All animals are muktza on Shabbat, even pets, since they do not have a practical use. Moving the animal or its fur or picking up an animal is a violation of muktza.
Reason Originally, all animals were owned for specific practical purposes (cats to catch mice, dogs for protections, horses for traveling...) and they were not used as pets as they are today (for companionship, to pet, etc). Some poskim say that some pets are not muktza since they are similar to toys.