This is known as a "Hunting Cup" or "Stirrup Cup". They were used to have a drink before starting off a fox hunt, etc or starting off on a journey WHILE ON HORSEBACK. You were to drink all of the contents immediately (thus you didn't have a bottom to set the cup down).
They have been remade over the years. Still ever popular and collectible.
They have been found with dog, wolf, fox, deer but not limited to animals. They were popular 18th and 19th Century and elaborately made of silver, pewter and even porcelain.
I recommend a hands on inspection of these to determine age/authenticity of an older one.