What you'll be doing as a dad
Picking random crap up off the floor—or snagging a cold beverage from the bottom shelf of your refrigerator—while holding your child in one arm.
What you need to build
Your quads and core, which will allow you to descend in a straight, steady motion without your baby toppling forward out of your grasp. (Trust me, the kid's mother will never let you hear the end of it.)
Dumbbell/goblet squats. The point is to keep your back as straight as possible, so you may want to practice without weights until your form is perfect. Once you've got it down, I suggest these two variations: Squatting with a pair of 25-pound dumbbells held vertically against your chest (3 sets x 8, increasing dumbbell weight as necessary), and squatting with a 45-pound weight plate held directly over your head (3 sets x 8, increasing reps as necessary). Get good at this, and balancing an infant will seem like a piece of cake.