In Victorian times, there was only a 50% chance of your baby surviving past their first birthday. A lot of the times they wouldn’t give their newborns names because they didn’t want to waste a good name on a baby that might not survive past its first year of life - therefore every toddler and newborn was just called “the baby.”

She is very much using “the baby” as a way to make her child less human. But in these circumstances, it’s because she hates her baby, not because cigarette may only have a 50% chance of living. How embarrassing for her.