Well, I definitely believe that you have what it takes to break into the pet photography business, and that is a love for animals.
I can just say "ditto" as to what others have said. For me, business jumped when I joined a golden retriever meetup group and started interacting with other pet owners. (yes, we own a golden retriever, so insert your own breed here) Volunteer, get to know other dog owners and things will begin to take off. You can find breed specific meetup groups at meetup dot com. We also volunteer our time and $$$ to local rescue groups. The groups in turn spread the word that we support them and then people started supporting us. Its not easy, but word of mouth advertising, coupled with great customer service is how any small business is going to survive these days.
Good luck!