Pet photography should not be limited to just dogs. If you have a unique pet such as a rat, or a guinea pig, maybe a chameleon - you can definitely set up a photo shoot for this pet.
If you want to try at home its always a good idea to create an "island" that the pet can go on - a raised surface that will contain the pet - or at least give you the opportunity to get it before it clambers off. Then you can add props. For a rat, because they are so inquisitive you can add seasonal items like a pumpkin for halloween or other holiday props. They will inevitably climb all over it. Then with a rat all you have to do is get some really smelly treat and wave it around and they will look in your direction.
Remember to place your "set" in good light and be ready to move around to capture the best shot.
If the thought of doing it yourself is too daunting - drop me a line and lets schedule your pets first photo shoot! firstname.lastname@example.org