Since you are quoting a question, you need to put the question mark within the quotation marks. It is a quoted question.
Ex: "What time is it?" she asked. [From your example itself]
But in cases where you are questioning a given statement, then you need to put the question mark outside the quotation marks. The entire statement is in question here.
Ex: Did she ask, "it is noon already"?
When a given statement and quoted words are both questions, put the question mark within the quotation marks.
Ex: Did she ask, "what time is it?"