They were commonly used as a model for 'companion toys' in Europe The first one below is from the mid-1900s. The second one is antique (probably circa 1910). Both from Germany.
Assuming it is a Borzoi companion toy it will probably be rabbit fur on a wooden frame, sometimes with a wire armature such that it can be posed. The legs are usually carved wood, but sometimes covered in felt. Very occasionally they have wheels so they can be used like a ‘pull-along’ toy but more usually they were intended as fashionable companion pieces for costume dolls (adult dolls, not baby dolls) and notably produced in Germany, Italy and France.
Borzois reached Western Europe from Russia where they were very much an aristocratic hunting dog, especially for wolf-hunting. During the time of the Tsars you couldn’t buy one, but the Tsars gifted them to people who had earned favour in Court. Enough of them had been taken out of Russia during the late 1800s to establish breeding stock elsewhere and they became more readily available after the fall of the Tsars in 1917. Although still used as hunting dogs, including for foxes, in the West they also became a status symbol for their owners and that extended to them being made as doll companions.
You know Roy Rogers stuffed and mounted his horse, Trigger. If I recall, at the time Dale Evans said she'd like the same treatment from Roy, just not necessarily in that order.