In reference to her hairstyle, this is known as One Bun; a Two Bun version was also produced.
These were early figural frogs that actually were not originally intended to be flower frogs; they were lamp parts. The one & two bun figurines are in two parts: the figural part has a glass screw bottom, while the square base has a 1" diameter glass threaded peg that is surrounded by a metal sleeve press fitted into the base so the figurine can actually rotate 360 degrees.
They are a bit hard to find. They were easily snapped at the screw and prone to rust.