Hello Robin. I adore your name!
Well, the term fascinator means something different than it did many decades ago when it referred to type of a knitted head scarf. Your little topper dates from the period of late 1950s to early 1960s. Back then it would have been referred to as perhaps a "whimsy" or a flowered cage veil. Today many new collectors use the term fascinator for the hat you show.
The veil type is really just standard millinery veiling, perhaps a Russian veiling, or cage veiling, with an artificial flower.
It looks darling the way you show it. Back in the day it sat more on the center of the head or back. But I like it better your way!