It sounds like there is some context missing from the question. It sounds like one part of a multipart question, the sort that involve a large chemical scheme with many unknowns, which provides more clues as to what Q and R might be.
Your logic that oxides of Q will be acidic because Q must me a non-metal is fine, but this only narrows it down to C, D, or E.
Without more information, answering this question relies on you recognizing what the cherry red QCl2 is. If you don't know, you can probably have a good guess: If Q is a non-metal and forms QCl2 (i.e. oxidation state of Q is +2), then which group of the periodic table is it likely to come from?