Well obviously a student on a QXC should not be using a GPS - that's cheating.
In fact the mere mention of the possibility of thinking of getting a GPS within the earshot of an instructor, prior to getting one's PPL, is a very bad thing to do because he's likely to regard you as a bit of a smart ***e and will be watching you extra carefully.
However, a QXC is usually a well worn and easy route, done on perfect days, not requiring any accurate nav to avoid a CAS bust (because that would reflect on the instructor) and one has to do it only once per life
If I was lost, I would do a fix with two VORs. Just tune in each one, turn the knob until the bar is centred with the FROM flag showing, read off the radial off the top of the dial, and repeat for the 2nd one. Then draw the two lines on the map and see where they cross. Takes a lot less time than calling somebody on the radio, and every PPL should know how to do this (and how to track a VOR). It's REALLY EASY. Even easier with a DME