I think this idea is great. I see as
the pros:
no one or not many people are already doing this at least from my experience and knowledge.
It would be relatively inexpensive and easy to get going as well as easy to market. Tons of people have cats and dogs. If you are good enough I might even want you to take pics of my dogs. Lol!

Cons:
Depending upon where you live and the city and county rules as well as any rules imposed by your place of residence you may need more licenses than you would want to bother with or you may not be able to do it out of your residence at all. I would check on this first.
I would also be careful about just going to anyone's home just because they say they are interested. This could end of dangerous. You will also want liability insurance if anyone decides to sue you over anything.