I think this might depend on where you live. In Los Angeles or NYC, you'd probably find a lot of people willing to pay for that service, but in smaller towns I doubt there would be much demand for massage services for dogs.
Also, like any other business, you'd have to have a great marketing plan to succeed... even in big cities, clients won't come knocking on your door, you have to go out and get them!
If there's a dog physical therapy clinic near where you live, they'd probably be able to give you an idea of whether there would be interest in that type of service in your area... or maybe they'd even want to hire you once you finish your course!
Good luck!