Thanks for all the input everyone! Quint's hat is far from a basic army cap. A friend of mine who collects WWII uniforms has one that's almost identical. The brim is a little more square and the stitching doesn't go through the front pocket. His (my friend's, not Quint's) is an Army Air Corps model A-1. It's a $100 hat, and it's WAY too small for me, so I'm going to use a faded baseball hat. I found lots of waterproof and oilskin hats online that were similar but I didn't have time to order one.
I'm just dressing up for kicks and to get a free popcorn at the theater – not quite worth me losing a $100 rare hat, but it'll be fun!