I saw today that the new movie Australia is going to have a large number of hats of the old Aussie type. These were made by Australia's version of the John B. Stetson hat company, "Akubra."
"An iconic Australian company had to research its own history for Baz Luhrmann's epic drama "Australia" starring Nicole Kidman and Hugh Jackman. Sydney-based milliner Rosie Boylan contacted Akubra over two years ago, wanting hats the company hadn't made for some time. Over 20 different styles, ranging from military to period hats of the era, were made especially for the film."
I mostly wear Stetsons, but I do own an Akubra hat, and the wife has worn one as her primary hat for nearly a decade. They're rabbit fur felt (Aussies are always looking for another excuse to slaughter rabbits), and so not very waterproof -- but lightweight, and good desert hats. I may order one of their old military style hats for this deployment, in fact, once the (wet) winter months pass, and the heat starts kicking up. Beaver felt is better for the cold and rainy months, but heavy for the desert summer.
If you're inspired by the movie to want one of these things, the only American company to sell Akubra hats is David Morgan's company on the West coast. Don't buy from him. He charges way too much. Thanks to the miracle of the internet (and easy currency conversion via MasterCard and Visa) you can order directly from The Strand Hatters in Sydney.
If you like Fedora (or Indiana Jones) style hats, they have quite a few of these; as well as some American Western designs, and of course the classic Aussie hats. As long as the rabbit fur felt is adequate for your needs, they're sturdy, fairly cheap, and long-lasting.