This one's from Bauhaus, the European home improvement chain (not the German art school). They have a store near Marcia & Rutger, so we've made many, many visits there over the years.
Bauhaus sells a wide range of little cabins and sheds. This model is appropriately called Lillevilla. It has a couple of things going for it. First, it's about the exact size I had envisioned, 1.8 by 2.4 meters, giving a bit over 4 square meters of interior space. Secondly, the price is right, it's fairly cheap at 4995 kronor.
The biggest downside is that it's pretty flimsy. The walls are only 16mm thick. (That's a bit over ½ an inch.) As Rutger puts it, you can't really hang much on the inside, a nail would go right through. I also worry that exposed life on the island will be pretty tough on such a thin structure. (For comparison, the walls on the little house are 66mm, and the big house, 140mm.)
I think we'll have to go a little bit bigger, or sturdier at least. Fortunately, there are a lot of options out there, and we'll look at another in the next episode of "The Shedhunter"!
UPDATE: I thought I had read that the walls on the Lunar Module were very thin, and I was right, much of it was less than a ¼ inch thick. (It is ironic that I spent time today, of all days, looking at Apollo info on the web!) Unfortunately, in my research, I came across many "moon landing is a hoax" websites, which really annoyed me. Idiots.