Erin Erickson from Dog Under My Desk shares a tutorial at Pellon showing how to make a dog bed with a removable fleece cover. If your doggie is especially spoiled, you could also use Minky. The cover has an easy to sew envelope closure. When the cover gets dirty, just remove the insert and run it through the wash. She gives the one she made a giant mustache applique. Go to her tutorial to see how to make one.
[photo from Dog Under My Desk on Pellon blog]