As someone has already noted, the spaces within the filename may be a problem (if not in GIMP, then likely elsewhere). Suggestion: where you have spaces, use an underscore (do_it_like_this.jpg). On my US keyboard, it is the shifted version of the dash ("-") key.

Also, I blew up your image, and it looked like there might be a space before the ".Jpeg" That's a bad place for a space. Also, one normally uses all caps or all smalls for file extensions (.jpeg, .JPG, and the like - your j is a capital J, but the rest are smalls. I don't know if that is a problem or not - it ought not to be, but...

Thirdly, as someone also noted, your image seems to have transparency - .jpeg does not do that, as far as I know. .png does. Wikipedia: "Raster file formats that support transparency include GIF, PNG, BMP, TIFF, and JPEG 2000,"
If you use something less used, like JPEG 2000, then make sure that it is usable where you intend to use it...

I have finished a design. Now I need to export in a Jpeg file. However, when I attempt to export I get a notice box;

[ The given filename does not have any known file extension. Please enter a known file extension or select a file format from the file format list.]

See attached

Attachments:

*> http://www.gimpusers.com/system/attachments/810/original/Export.PNG