There also appears to be a loop at the very top of the crescent, and at each end I think I can see a small diamond crown. Am I right?
I believe this unknown brooch could well be a sarpech (aigrette) worn originally on a royal turban. In the picture below you can see the hanging emeralds above this rajah's forehead.
(Photo credit unknown)
The Queen's "new" brooch could possibly date back to her grandparents' visit to India for the Delhi Durbar, or even further back - to Queen Victoria, who was know to have a passion for all things Indian.