I am so sorry for your loss!!
I think it's great that you have the opportunity to get one of his pups. As far as newborn and pup go, I have actually experienced that. I was going to suggest that you bring the pup home first, which it seems you've already decided on. I feel like that way, you have time to establish the order of the pack before baby arrives. I agree with previous poster about never leaving baby and pup alone either, I also think it will be good for your other dog to have the new pup to bond with. Especially since baby is coming too.
Another way to think of it, is the puppy will get you guys ready for night feedings when you have to get up to take him or her out. Then when baby arrives and gets up to eat in the night, you can take the puppy out too.
Congratulations on your newborn arriving in December. I will be sending my thoughts and prayers to your family and the others that have lost their fur babies recently.
Sent from my iPhone using Tapatalk