I agree with Anna Marie. But maybe you are trying to say that the question is TOO inquisitive and thus rude. If you are trying to say that the question is rude because it asks the person something too personal, you can say “an inappropriate question” or “an indelicate question.” If you are trying to say that the questioner should not be asking the question — for example, because he is pressing a superior for an answer in some situation in which he should just follow directions — you can say “an impertinent question.”

It’s redundant in this context. Inquisitive, by definition, means you’re wanting more information or are curious. More commonly, inquisitive is used to describe people.