Is that a cat? Yes, it is. No, it isn't. Is this a cat? Yes, it is. No, it isn't. Is that your brother? Yes, it is. No, it isn't. Is that your sister? Yes, it is. No, it isn't. As you can see, the subject of the answer is always 'it'. Whether it's near or far, an object, a person or an animal....the singular subject of a short answer is 'it'.

Good day! Is that a cat? Yes, that's a cat. No, that's not a cat. Your short answers are okay, but this is better English. :-)

Because the question contains the demonstrative "that", we already know which thing we are talking about, and we don't need to repeat the demonstrative "that" in the answer. "Yes, it is", "No, it isn't"

"That" sounds a little odd-there is no need to specify "that" since it is very clear what you are talking about.I would just say, "Yes,it is." or "Yes:" and then add some information like "It is my neighbour's".