With most (all?)browsers, and with most (all?)versions of Windows, one of the easiest ways to put a website shortcut onto your desktop is to go to the relevant site and then reduce the size of your browser window slightly (by clicking on the overlapping squares at the top right), so that you can see some of the desktop as well.
Then click-and-drag the symbol which appears immediately to the left of 'www' (in the browser's address bar), pulling it onto the desktop. Job done.
Have you tried that method?
However I wouldn't want my desktop cluttered up with internet shortcuts anyway. That's what bookmarks are for!