Export is for exporting Titles. You want Publish+Share towards the top right of the screen. Once you've selected it you have to look carefully to spot the scroll bars with which you can see all the available sharing options.
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What version of Premiere Elements are you using and on what computer operating system is it running?
Do you presently have Premiere Elements 7 which includes the File Menu/Export/Movie and is that what is not working? Or, do you have a later version of Premiere Elements in which the File Menu/Export/Movie is no longer available, instead only File Menu/Export/Title?
What is your plan for getting your video to Facebook
a. export your Timeline to a file saved to the computer hard drive and then upload that file to Facebook at the Facebook web site?
b. use the Premiere Elements upload of your Timeline content to Facebook from within the Premiere Elements sharing area (called Share/Computer/Online/ in version earlier than 11 or Publish+Share/Online/ for version 11 or Publish+Share/Social Websites/ for version 12?
Have you coordinated your plans with the Facebook requirements for uploading videos to it.
Please review the above and then let us know if you have questions or need clarification on anything written.