I am with Sago on this, it rather depends on how and where you are using the term.
I might describe Dh's car as his 'baby', not in any serious sense but just because it is old and a bit crochetty and is always going wrong and demands a lot of his time and needs a lot of nurturing, just as a baby does. I am certainly not suggesting in anyway that he cares about the car as he would care about a baby,
The term 'baby' is often used to describe something smaller and cut down from a larger item.
I think, in fact the word has two meetings, one to describe something that is the dimunitive version of something bigger, or some object that is very time consuming , and th other meaning is a word used to decribe a young human being,
When people take the second meaning - that of a young human being and applie it to a dog or other object because they are equating the dog and the baby - then, yes, yuk. Other meanings I have no problems with.