Do you sew? You could make something like it out of fleece, using heavy interfacing on the brim and taking a few hand stitches between the crown and brim to keep it in place.
View D of McCall 3400
might work, though I think a pattern that uses four petal shaped pieces for the crown might be better. There's a free one online from EZ Fit
; I didn't love it (you can read my review here
for more info). You can also download the free version of Wild Ginger
, which has a hat pattern. I don't remember if it has a petal shaped one or not; I made a sunhat of the one that has a circle crown and brim.