Just as a data point, I used the iron-in version of Pellon Flex foam for some rectangular "bins" for our closet shelves. They came out fairly floppy, particularly the long sides. It would depend on how large the doll bassinette was, but I don't think the foam is rigid enough on its own. It would need additional structure of some sort. For our closet bins, adding stiff wire seemed to be the best solution.