What's the correct punctuation for quoting a question within a sentence?

Something like:

When addressing the question, ‘What should I wear today?’, one must think about…

What should be done about the question mark vis-a-vis the comma? Oxford Style Manual states that you should use punctuation in both the embedded quote and the enclosing sentence, but only in the specific case of terminal punctuation where it serves equal but different functions, e.g. Did he really shout ‘Stop thief!’?

No conjecture, please. Oxford Style Manual rules preferred, but CMoS will work as well. Looking for an “official” answer.