On the long lifespan, they are babies for about 4 times as long. I'm not sure of the exact length; I was just planning on asking the same question.
I'm currently playing on long. A few days after birth, I got a notification that the baby's birthday was soon. About a week later, I got the notification that today was his birthday. He then stayed a baby for four more days before auto-aging to child. In all, I think he was a baby for about twelve days, but my sims had a second child in that time and I lost track of which day things happened on. I think the notifications are tied to milestones in the normal lifespan, so on long they are happening too early (four times the number of days too early).
I did notice that the notification times and the time the baby aged up were about the same time of day, and about the same time of day as the birth had been. For the first child, that was evening, and the second was at noon.