I think you would be better off doing all the available photography that you're good at, or that you can handle.

I have a pet photography studio in a city in North Louisiana, and I don't make a ton of money on it. People just don't expect to pay a ton of money on thier pets for something like photography. All the money I really make from just doing pet stuff comes from holidays. But if it's just during the regular season I don't see a ton of business. BUT...that's why I do all sorts of photography stuff, I don't just do pets, I do pretty much everything else but weddings, and I live comfortably.

It takes ALOT of word of mouth and advertising to really get everything going though. If you don't have people seeing your stuff out there you won't get much business, but then that applies to all business. I'm not trying to discourage you from starting your own pet photography business because really it all depends on the area you live in, around here there just isn't a really huge market for that type of thing. I'm the only one I know of in my area that does it on a regular basis though.

And there are PLENTY of people that have pet photography businesses that make it. Here's a couple examples.

http://www.dogumentarian.com/

http://www.bryantdogphotography.com/