I will second Eric Andres's point in using "querer" with living creatures instead of "gustar."
At least in much of Latin America, using "gustar" with humans usually insinuates a physical/sexual attraction. With animals, even though it's (generally) certain that you're not saying that you find the cat sexually attractive, it might sound slightly off. Best to err on the side of certainty and use "caer bien."
"Caer bien [a alguien]" is closer in line with the way we use "like" in English when referring to another person, and can be used with an individual animal. Querer is a bit stronger, like a light version of "love." (The "Querer vs. Amar" discussion is another great topic, but not directly on topic in this thread.)
For this reason, "el gato me cae bien" or "me cae bien el gato" would sound more natural than gustar.
My background: I'm a native English speaker married to a native Spanish speaker. I have been fluent for 13 years, a certified healthcare interpreter for 5 years, and came to Stack Exchange to continue refining the fine details and nuances :)