Yes, we do! We have sitters who care for cats, rabbits, guinea pigs, birds, horses and reptiles, just to name a few.
However, at the moment we don't have a way to show a sitter's profile for a particular type of animal. So we recommend clearly listing the types of pets that you are willing to care for in your profile description.
If you only look after one type of pet, you can make this even more apparent by mentioning this in your profile title. For example "Jane's Cat Paradise" or "Jane's small critter care".