There is no way that you can use QRegExp to validate a date, even when using the more advanced features like assertions (e.g. looking forward). I think the best you can do is use the QRegExp to restrict the format of the input and then validate afterwards.
Go back to the requirements specification for the question. If it is vague, say so in your assignment. If it lacks information, make an assumption and state that in your assignment too. This is a third level course, you're supposed to show you can think for yourself not just produce output like a robot. Showing your thought process can help a lot.