Hmm... the only times I recall her wearing any kind of hat... twice in the pilot (a fedora in the rain, and a wide-brimmed hat in the 1880s), and she had a scarf at the beginning of "End of Nights."

This is her in a hat looking vintage. :D I wish the show would give a solid date for when she became brunette (she's brunette with Amelia Earhart, so before 1920-30). But still. :D