If you weren't so far on (as in still in first trimester) I'd say that possibly not too bonkers. However, if you got the puppy tomorrow you'd just about be getting to a point where there was a vague degree of confidence in his/ her new life and the housetraining getting on for more reliable when the pup's whole life would be majorly disrupted which wouldn't be fair and would quite probably unless handled in an expert manner lead to behaviour problems just when you don't need them. Dogs challenge at different times in their development and this potentially could be a horrible clash with pup pushing boundaries and you not unreasonably being absorbed with baby, trouble, trouble, trouble.
Also, pup would start needing longer walks and training just as you are trying to juggle late pregnancy then baby. Just imagine you, the buggy, a small fractious old baby, and an 9 month old bouncy labrador wanting to go say hello/ explore on the end of the lead....... Labs can weigh a tonne and unless you have money to burn on dog walkers and trainers to do the job of establishing a brillant recall at a very early age and perfect non pulling heel lead work at the same, plus the time to put effort into taking over that training..... it requires little imagination to see how bad a combo that could be.....
All of this is just if everything is normal, going averagely and no major issues!
I'm 35 weeks and adore my little dog but am struggling as he's really been traumatised by fireworks this year and won't go out after dark. It has also made him funny about when he "goes" and to avoid accidents in the house I've spent the last few days having to go for much longer walks than I'm comfortable walking for (about 4-5 miles in total yesterday...) as bangs in the distance etc, etc, etc have stopped him in his tracks at inconvenient times and it has taken him ages to calm down enough to get on with it. Poor little guy, although I have help from relatives who walk him as well I feel he's my responsibility so it is up to me to make sure that he is in a position to make it through the night comfortably as he won't go out after dark. Sorry for slightly grizzly example but it does rather illustrate that stuff doesn't always go to plan thing!!
Sorry for ramble but think it might be a real toughie for all of you and maybe waiting until baby is out and a bit older and more robust would be better for you!