Hi,
I have a few pieces of faux coral items, dress clips, a hat pin and a few brooches. Mine are all from the later 1910's to 1930's. All of the pieces I have seen from pre 1930s have the coral (plastic, etc) set in prongs, some sort of setting or bezel. Yours looks glued on (?). I suspect that maybe your brooch is a marriage between an older backing and a later plastic coral piece. The metal part looks older, and the glued coral looks added to me. Of course I certainly could be wrong as I am not a jewelry expert, just have seen a lot over the years.
I took a second look and is that metal marked sterling on the back? If so it could be a gold wash over sterling, so a plastic coral is an odd match.
I can say it is charming and very sweet.