Others have said it, and you will get varying opinions, but here is my take.
For background I'm 33 and have 3 kids. 10, 7, and 3. First kid my wife was a wreck with postpartum depression, scared for our son (had some health issues early), and just completely exhausted.
At 1 month out you could have a happy rested wife and child, or you could have a stressed, exhausted, panicky wife that is scared to death something will go wrong with your new baby.
My advice for what it's worth. Talk with your wife again and explain things this way. Tell her you would love to go turkey hunting in the spring if everything works out, that it would be a short outing if it happens. BUT explain that she is your #1 priority and the baby will be once it comes as well. And tell her you are 100% prepared not to go if there is anything wrong at all, including her being tired and overwhelmed.
I screwed up with our first kid and didn't take care of my wife enough, didn't know any better! Did much better with the next 2 and now I hunt when I want and take the kids when they can go. My wife is amazing and we both give and take. But pregnancy and delivery are major turama events to a woman's body and depending on how she does she may need you home!