Sandy,
Well, that IS interesting! It reminds me of those antique Chinese sewing baskets, with the lid partially removed. The hat is straw and has what is called a bumper brim or roller brim. You might call it a novelty straw hat, or basket hat? Not sure on this odd one! As for the era, I cannot tell from the photos, but can you show the interior? That will give clues. It looks fairly contemporary, and from the look of the straw was probably made in China for the mass department store trade such as Target, etc.