I think you're in a pickle! I also have no kids, and I think having a new pup and a new baby at the same time is a bit overwhelming. I had a hard enough time with just a new dog. (not a puppy) To be honest, he's special and needed special attention. But now that he's settled in nicely,(he's been here 2 years and he's 3 years old) and I know what his triggers are, I might be able to balance both him and a new addition. (either skin or fur)
If you have to add a pup to your life now, I'd do it before the baby comes. That way you can bond and get to know him/her. He/she will learn the rules of the house and the transition to baby may go smoother. My honest advice would be to wait a few years. The new baby is on it's way, and you can't return a baby!
Potty training a pup, sleepless nights with the baby, you're going to be spread pretty thin.