"질문을 대답하는 것 좋아요!" => "질문에 대답하는 것(은/이) 좋아요!".
In Korean, we say 질문에 대답하다 with 에, and never 질문을 대답하다.
The reason for this is probably because 대답하다 (and similar 답하다, 응답하다) is already a compound word.
It is a short form for 대답을 하다(give an answer). For example, you can say 긴 대답을 하다 (give a long answer).
Since 대답을 하다 is already in O+V form, taking another object will make it 질문을 대답을 하다, an awkward form.
So you can only say 질문에 대답을 하다, and for consistency 질문에 대답하다 as well.
On the other hand, We say 질문을 하다(ask a question) and 질문을 받다 (be asked a question).
In these cases, 하다 and 받다 are unbreakable unit words, so they can take a direct object with 을.
But all this is just a matter of getting used to the right expression. No need to get into the reason too much.