"Quick question" vs. "short question"

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.

In everyday usage . . .

"Quick question?"

is a common expression and is a way for the asker to indicate to the askee that they are asking for a brief moment of their time - implying an "interruption" for a question but that by its brevity, should not take too much of their time.

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.

"I have quick question" invariably is a clue to me the questioner doesn't understand that the answer will be long and involved. In fact, in my experience, "just a quick question" is an excuse to interrupt.