Dunny are similar to Qee, and while they are not as old as Qee they have pretty much bumped Qee out of the US market. They are made by Kid Robot, a toy and clothing store based out of New York.
I own only a few of these, most of which I bought during a visit to the Kid Robot store in Soho. I will most likely never purchase more of these, but I do like the ones I have.
Here is my collection so far (click to enlarge images):