I agree completely. I don't care if your pet is a substitute for a child. It. Is. An. Animal. And unless it is under 6 months of age, it is not a baby.
Another one that is like nails on a chalkboard for me is the euphemism "over the Rainbow bridge". Where did that even come from? When I first heard it I thought it referred to a destination for the LGBT crowd.

Call a spade a spade. Your pet died. It is no more. It has ceased to be. It is bereft of life. It is an ex-pet. (insert your favourite Monte Python phrase here). It is no longer pining for the fjords.