If you drag a link or favicon on the left end of the location bar onto the desktop to create an internet shortcut then that shortcut gets the icon of the default browser.

If you want a different icon (favicon) then you have to assign that icon yourself to the desktop shortcut (right-click: Properties).

You can usually get the favicon if you append "favicon.ico" to the main domain of a website (e.g. http://www.mozilla.com/favicon.ico ) to display the favicon in a tab and save that image to a folder or see if you can find it in "Tools > Page Info > Media".

When I saved it it didn't show up as an icon. When I went back to save it with the extension .ico that didn't work either.

Any other ideas.

That is an animated GIF image (18 frames) and probably can't be set as a shortcut icon for that reason.