。
She asked me a question.
Literal
She [topic-は] me [to-に] question [object-を] did.
質問をする ('to ask a question,' literally 'to do a question') is one of the many 'noun + する' constructions where する acts as a light verb taking the action-noun as direct object. Distinct from 質問する ('to question'), where the same noun is verbed directly. Both are correct; the をする version is slightly more deliberate, often used when you want to slip in modifiers (重要な質問をする 'ask an important question').