This countable noun, with alternative forms fur kid and fur-kid, is used to refer to a pet that is treated as though it were someone's child. In the late seventies, the word pet was argued to be politically incorrect by animal-rights activists, since it implied human ownership of an animal, and the alternative phrase companion animal was suggested. In the noughties, it seems, we've gone one step further and introduced a term which goes beyond the idea of an animal as a mere companion, elevating its status to that of a kind of surrogate child: the furkid.
'Couples like furkids because they usually don't live long enough to need expensive private schools. And their friends like furkids because, unlike real children, you can plausibly claim to be allergic to them.'
(ABC Network, Australia, 2004)