What you'll be doing as a dad
Carrying your baby in a car/stroller seat. (Like this. Doesn't he look happy? Man, fatherhood is such a gift.)
What you need to build
Your delts and traps. Unless your job involves moving paint cans or buckets of water, you will be shocked at how unprepared you are to have weight hanging directly from the side of your body, and how quickly your shoulders start screaming for mercy.
Upright rows. You're going for endurance here, so use slightly smaller weights—say, a pair of 20-pound dumbbells to start—in three sets of 15. If that's not challenging enough, add weight. The front raise is another great exercise that hits the same muscles and closely mimics the motion of lifting the baby/car seat in and out of your vehicle. Once you’re able to do that without grunting audibly, pat yourself on the back and crack a beer; you’ve earned it, dad.