I just took a look at this issue with my version of Premiere Elements 11. I'll start by saying that I was using an NTSC codec and have Premiere Pro installed on my machine (along with all of the codecs that get installed along with it). With that in mind, I was able to do what you're wanting to by going to the "Publish and Share" drop down menu and selecting "Computer". From there, I was able to scroll down on the presets list to QuickTime (which is another way to say .mov). Within the QuickTime preset I went straight to the "Advanced" button below the "Save In" dialog box and clicked on it. This brings up a number of options that will allow us to get you the best video quality along with the frame rate that you would like to use. Within the "Export Settings" window that pops up, click on the "Preset" drop down menu and choose a setting that is appropriate for the size of your original video clip.
The next step is the most important. Scroll down to the "Video" tab at the bottom of the "Export Settings" window. You'll find a "Quality" slider. Crank that slider to 100 for best rendering results. Next, scroll down even further in the "Video" tab until you see "Frame Rate". Select 25. If there is no drop down box where the "Frame Rate" field is, the preset you have chose isn't then allowing you to change this parameter. To fix this change your preset to something similar to what you've already chosen. Lastly, hit the check box next to "Render at Maximum Depth" to get the best color quality in your video.
Hopefully that helps! I'm not sure if Adobe Premiere Elements 10 and 11 are similar enough for my step-by-step guide to work perfectly, but I hope you get the idea regardless. Have fun editing!