Did Cleopatra have a greyhound?

No, Cleopatra could not possibly have a greyhound, because the greyhound as we know it, originated with the Celts. The hounds shown on many Egyptian tombs are believed to be Saluki, originating in ancient Persia. There is also another breed of dog popular in ancient Egypt called today a Pharaoh Hound. This and the Saluki may be the same.