MOV is a wrapper, what is inside YOUR wrapper - Exactly what is INSIDE the video you are editing?
Codec & Format information, with 2 links inside for you to read http://forums.adobe.com/thread/1270588
Report back with the codec details of your file, use the programs below... A screen shot works well to SHOW people what you are doing
https://forums.adobe.com/thread/1070933 for screen shot instructions
Free programs to get file information for PC/Mac http://mediaarea.net/en/MediaInfo/Download
Does your video use a VARIABLE Frame Rate or a Constant Frame Rate?
-below says Mac (Win process should be the same) but even GoPro says to convert to edit
-use to convert http://gopro.com/software-app/cineform-studio/
What is this other application in which you get video and audio viewing of this GoPro file (presumed H.264.mov (1080p30)?
Do you have the latest version of QuickTime installed on your computer along with Premiere Elements 13? Please do check
to make sure that presets are displayed for the QuickTime choice.
Use the thin scroll bar to the right of those choices to scroll down to QuickTime in the list of Publish+Share/Computer/ choices
until you get to QuickTime.
Are you running Premiere Elements 12 and QuickTime as Administrator?
We will be watching for your follow up.