Hi,
Happy to help. The term "body" refers to the fur felt blank used to make the hat (it would later be blocked and steamed into the desired shape, trimmed, sewn, etc) and was imported from Europe and is stamped to identify it as such. "Milady" is the trade or novelty name of the particular type of finish used on the felt, or a name for a line of felts used that season, or the name of the importer who sold the body to the hat making company. The hat itself (the finished product) was made in the USA. The designer label is licensed. Schiaparelli licensed her name to fashion accessories starting in the 1950s, including hats, which were all made right here in the USA by various makers.
I know, it sure seems confusing at first!
Adding this...I think it dates from circa 1960, give or take a year or two in either direction. Hard to tell exactly as the style is rather classic for that time period and remained popular for about 5-8 years. The finish on the felt is a plush finish.