+1 for the solution Backpacker suggests, if you absolutely have to do it. First solo isn't really the moment to fiddle with a camera in the cockpit.
You can rig a GoPro (ideally out of your view so you don't get tempted to adjust it during the flight!). Depending on the memory card, these things can record several hours of video, definitely more than your flight will last.
Anyway, good luck with your solo!