The general activity is driving, no matter the distance. You can qualify the trip as a 'short drive' if you really want to structure the sentence the way you did (but see a bit further down on other ways you might express the same thing). In general, English tends to prefer to use phrases like this to express specific concepts instead of using special words. There are, as with anything in English, exceptions to this practice, but you will almost always be understood if you choose to phrase things this way instead of using more specific nouns.
You might also hear 'short trip' used in the same way, which has largely the same meaning but doesn't necessarily imply that any particular vehicle (or any vehicle at all for that matter) was used, just that the person traveled a short distance from one location to the other.
However, I would probably not structure things this way in the first place. At least in the American Midwest, it's far more common when you're specifying both the point of origin and the destination to just say that you drove from the first location to the second location. So, your example might instead be better worded as "Yesterday I drove from Brooklyn to Queens". Note how this does not try to qualify the distance traveled, because that's usually implicitly known (or at least, generically understood) based on the two locations that were mentioned. This also can be easily extended to include the exact distance if required.
Going a bit further, if you were known to be somewhere specific at the time you started traveling to the destination, you might just omit the point of origin altogether and simply say you made a short drive to your destination. Using your example, if you were known to be in Brooklyn yesterday, you could instead say: 'I took a short drive to Queens yesterday."