fur baby
n.— «The comparative review of recent history to the present, and the changing status of dogs from living outside the home as working dogs on farms and as guard dogs, or serving as a distraction for the children in the family and perhaps as a means to teach responsibility, to the far more elevated status of a true member of the family, with new descriptive language like “pet parents” and the more recent coinage “fur baby,” is interesting and instructive.» —“A dog-centric America? A book review” by Mary Haight in Chicago Examiner Apr. 12, 2009. (source: Double-Tongued Dictionary)
Further reading
Language is always evolving, and that’s also true for American Sign Language. A century ago, the sign for “telephone” was one fist below your mouth and the other at your ear, as if you’re holding an old-fashioned candlestick...
Professional dog walkers call a dog obsessed with carrying sticks a branch manager. Another dog who grabs the other end of the stick and helps carry it around is jokingly called an assistant branch manager. This is part of a complete episode.
Related
I have long referred to my cat as my furbaby (fur baby). Your definition is exclusive to pet dogs. I think it should be broadened to include pet cats, as well.