Hi,
Wow. I would say the style is simply.... unusual! My initial guess judging just by the photos is it is a costume piece, part of a special order for a theatre or film, etc. The inside foundation does not look like any finished millinery construction style that I have come across. If it were a ready to wear hat from a millinery shop, etc., it should have a more substantial inner construction. Does the tiny paper tag give any hints? Is the inside material soft or is it more hard? Is the material plastic like, or is it a natural fiber like straw? As for dating I can only guess, maybe post WWII.
Definitely unusual!