A recent New York Times article, Bonding With Their Downward-Facing Humans, states that the practice of doga is increasing in popularity. The DogaDog webiste defines doga is defined as "yoga for you and your dog." While some feel that the doga detracts from the serious practice of yoga others think that dogs "are a natural match for yoga’s emphasis on union and connection with other beings."
There is no official certification program for doga instructors so finding a qualified instructor may be challenging. There have been a few books written on the subject. For example, Doga: Yoga for Dogs covers the major asanas (postures) from the Downward-Facing Dog to the relaxing Happy Puppy and restorative Pup's Pose. Each stretch is demonstrated by one of the dogis, with accompanying text to help people adapt positions to their own practice. Also included are breathing techniques such as the hot breath, or pant, and tips on practicing with your own dogi.
If you have a cat rather than a dog, don't feel completely left out. Take a look at Cat Yoga: Fitness and Flexibility for the Modern Feline . The author claims that the practice of yoga will help your cat feel more energetic -- that's something my cat could certainly use.