So I set about building him a dog house out of craft wood. I based it on the picture you see there. And yes, I know that Snoopy's doghouse has a peaked roof, but I needed it to be flat so that he could sit on it and the typewriter wouldn't slide off the side.
I like it and I'm very happy with how it turned out. I'm debating about putting it on a base with the words "It was a dark and stormy night." printed above him. I'm still undecided on that. It's done for now.