Which one would you prefer: "quick question" or "short question" for a question that you know is simple and will only take a moment to answer? Or maybe "simple question"? The problem I have with "quick question" is that I don't think a question may be "quick", because it is not moving anywhere.
What any of us might prefer is immaterial. A short question is one that contains only a few words. A quick question is one which the questioner hopes, perhaps unrealistically, can be readily dealt with. Quick has many meanings, and they are certainly not limited to describing a fast-moving object.
Quick, short and simple are all correct but mean different things. Quick just refers to it lasting a short time. A short question has few words and a simple question has little complexity.