Buckrum is a material actually used to make hats! If you make the hat, buckrum can be found at most fabric stores. It's not very hard to work with either. I used it to make the shoulder pieces on my Pacifica costume.
If you want more support you could always put wire around the edges to make it stiffer.
I've never made a hat before, so this is just going on my past experience with these materials. If your willing to experiment I would deffinately try the buckrum