Is it possible to use the GoPro Studio to make a video within a video type effect?

I plan on using my GoPro to record myself presenting material for a distance education class. I'd like to have a video of my presentation as the background and a video of myself discussing the material overlaying the background video and appearing in the corner as a much smaller video. My intent is to have a final product that looks like a Skype conversation.

Is it possible to do this in GoPro Studio or am I going to need a better video editing software? I'm familiar with Adobe Premiere Pro, but I'd rather not pay for it. If I can't use GoPro Studio, what video editing software do you all recommend? I'd prefer free or cheap.

Thanks!