"What time do you eat?"
It should probably be accepted unless they change "what time", which is relatively vague, to "what time of day" or add some hint indicating that the question is about the time of day as in "What time do you eat in the afternoon?"
One could presumably respond to "什麼時候" with "every day" or "Tuesday", but those would be bad responses since the questioner is apparently asking for a specific time of day.
It would make sense, but usually in Chinese you like to have two syllable phrases. So just saying 吃, feels kind of empty.
It has been awhile since I have studied Chinese, but can't you write 几点你吃饭?