This first post states inaccurate information. The correction is in the 3rd post down
Well, I finally figured out how to export an object from Blender, with alpha-transparency.
Select the object
Select "file" > "save rendered image" (do not have an opened render window)
Now, you should have a copy of that image, in which ever format you chose, i.e. png, jpg, etc, where ever you save your rendered images to.. be it /home/yourname/Pictures, or so on.
The overall size of the image, will depend on which size rendering area you chose as well, like 1280x1024, 800x600, etc. But the background will be transparent.. and now, you can use that image in any app you want to make a new desktop wallpaper, etc. within Gimp, Inkscape, XaraLX, or what ever your favorite Linux graphics software may be.
Here is an example of what I am yappin' about