I'm not a Tinder expert by any stretch of the imagination... I have done some Tinder and IG game successfully though.
And from my experience, unless you're really hot in your pics, putting all of the emphasis on making them carry the initial conversation is just a bad strategy, in general.
I don't necessarily think it's a bad question but if you were to ask a question, you'd probably want a low investment question like... "coffee or tea?" - then you could get into the would you rather game from that...
But you're probably better off starting with a relevant statement to something going on in their profile than a generic question that could be copy/pasted to lots of women (and trust me, they know you're doing that)... which means the ones responding with one word answers are giving you the same amount of investment as you're giving them, which is practically nothing and not very interesting at all, btw.
I've talked with a lot of people with their Tinder strategies... most guys I know who are successful fall into one of two categories... category one guys cut the bullshit and get straight to the point very quickly by saying something to gauge their interest and then immediately trying to get them out.
Category two guys are good at texting and getting a girl engaged, feeling comfortable, and then get her out.
My guess is that you're not a category two guy, no offense, lol. I'm not either. I'm much better in person than I am over text.
I'm not sure where you came up with the question that you're using but if I were you, I'd model someone who is successful with Tinder game and go from there.
To answer your question though, at least in person, if a girl gives you an answer like that, and it's beginning of the seduction process, the best thing that I've found to do is just improvise off of it before asking another question... otherwise, you're relying on her to do the bulk of carrying the conversation, which she has no particular reason to do.
You're just another boring guy who doesn't know how to talk to her, as far as she's concerned.
But you could do a couple things with that...
One is a cold read... "Hmm... cats, very interesting... if you're into cats that probably means that you're the type of person who may know a lot of people but you only let a select few get close to you. But when you do open up to them, you really open up."
Or play off of her looks... "Now that you mention it, you do kind of have cat eyes in your photo... big but a little suspicious... like you're up to no good."
You could show a preference... "I'm a dog guy... wait, does like attract like or do opposites attract? I think this means we're either going to be best friends... or mortal enemies!"
You could also tell a personal story, or do a host of other things there. And then go into asking her a question from there.
Doesn't that seem like it would be a lot more interesting to her than just asking her questions and hoping she'll carry the whole conversation?
Like I said, I'm not a Tinder expert but if this was in person, that's what I would do.
I hope that helps.