Those are not only contradictory, but lacking information. 1920x1080...AND 720? Makes no sense. The video needs to be either 1920x1080, or 1280x720. Can't have 1920x1080 that's 720p.
Quicktime, by nature, is MOV format. But what codec do they want? I'm assuming H.264. So, you can compress to 1280x720 H.264 as a QT MOV. But how LONG is the piece? Because the quality of the export...the data rate...to get it to 200MB..depends on the duration of your video.