The Chicago Tribune has a good (and long) article on the rise of animal law as a specialty. More schools are teaching it, and there are more people out there practicing in this particular area.
I won't pretend it's not a pretty controversial area. I think what concerns most people is the question on standing. Do they have certain legal rights? Is not being beaten or killed a right for an animal, or is it the humane treatment that we owe them as stewards of the planet? It's a question that needs answering. Every time I see something dealing with animal law, I see comments from people talking about being sued by a German shepherd. Yes, it's silly, but that's how many people view this stuff.
If you can leave your estate to a dog, does it become a property owner? Doesn't that open up a can of worms. Next thing you know they'll be barking at you to get off their lawn!