Well, that is a great looking hat. And yes, Tricia, you are correct. It is a fez. It matters not that it does not sit atop the head like a Shriner's fez. It can be tiny like a clown's toy hat or sit low on the face like a bucket.....A fez is a fez is a fez!
We could use a few more clues. Are the beads glass, or are they a good quality plastic? Plastic is fine, many good milliners used black plastic jet beads on their hats in the 1950s to keep the hat more lightweight on the head. Also, is it wool, or is it a fur felt? And lastly, what is the hat's inner circumference? These answers will help us narrow down a date for you.
To answer your other question, the fez was at its most popular in the 1940s, more so towards the earlier pat of the decade. Yours looks somehow post WWII to me, maybe late 1940s, but I think it is 1950s. Hard to be sure without seeing it in person.
The Yaeger label looks 40s 50s to me. I have come across a number of hats with this same label, all were late 40s and 50s hats.
I would guess 1940s - 50s.