No quest. You can talk to animals if you get the pet related skill. I'm still exploring Fort Joy and the surrounding area. The cat seems to stay out of trouble except if you get close to one particular area. I haven't found anything important with the cat yet, but it might be worthwhile talking to the dog.
The dog leads to its own minor quest that gives you no experience. The cat is still bugged I started a new game again and spoke to the dog avoiding the cat. I had pet pal perk and that is why I said a fugue state the cat is confused when you speak to it. The reason I thought it might be an unimplemented quest since it follows you as that maybe you can find a way to cure it.
