beardy
n.β Β«Mary Lott of Salem lives with three bouncing, busy “beardies,” as the breed is called by its fans. Sheβs afraid that people will see the trained dog on the screenβand the puppets that play the dogβand buy these shaggy dogs on impulse.Β» ββThe high price of film fame” by Deb Wood The Oregonian (Portland) Mar. 14, 2006. (source: Double-Tongued Dictionary)
This term is also used for bearded dragons, a lizard native to central Australia.
http://www.tncbeardies.com/Care_Sheets.htm