beardy
n.— «Mary Lott of Salem lives with three bouncing, busy “beardies,” as the breed is called by its fans. She’s afraid that people will see the trained dog on the screen—and the puppets that play the dog—and buy these shaggy dogs on impulse.» —“The 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