1) Open iTunes and select the song that you want to copy to the desktop.
Click for full size
2) Right- or CTRL-click the desired song and select "Show in Finder" from the drop down menu. This will open the directory where your MP3 file is stored on your hard-drive.
3) Now you can retry to copy (ALT + drag and drop) the music file to your desktop!
If this still doesn't work, you should verify the permissions of your MP3 file.
1) Select the file and press CMD+i (CMD=Apple key). This is the shortcut for opening the "Get Info" panel!
Click for full size
2) Under "Sharing & Permissions:", the configuration for your account should be "Read & Write", not "Read only".
You may have to enter the admin password to be able to change the permissions.