I always learn something new here: I wasn't aware of the Private Character Editor until reading your post.
The characters you created are saved in C:\Windows\Fonts\EUDC.TTE
There's also a file named C:\Windows\Fonts\EUDC.EUF
You won't see either of these files if you use Windows Explorer to navigate to C:\Windows\Fonts because Fonts is a special folder and doesn't recognize those file extensions as fonts. However, if you search for EUDC.* you'll find them.
As far as copying the Private Characters to another computer, I don't know if simply copying both of those files to the C:\Windows\Fonts folder of another computer will result in Charmap showing "All Fonts (Private Characters)" at the top of the list.
I copied just EUDC.TTE to the Desktop of a Windows 7 computer, opened Control Panel > Fonts, and then dragged EUDC.TTE into Control Panel > Fonts. I didn't get "All Fonts (Private Characters)" but surprisingly a new font named EUDC Regular showed up in the list of fonts, and sure enough, that had the character that I had created.
The following may provide some help:
http://www.7tutorials.com/create-your-own-characters-private-character-editor