I believe they do, and that they're located along the spinal column in vertebrate animals, just like ours.
Though not all animals have the same number of cervical, thoracic, lumbar, sacral, and cocygeal vertebrae as we do. For instance, most animals have tails (coxygeal vertebrae).
With the right training you should be able to find them with your hands.
Doing energy healings/chakra alignments on pets would be a good practice. "Veterinary Energetic Healing".