First and foremost, plan to put the infant in the back seat along with someone who is capable of seeing to the infant's needs during the flight, and all the equipment neede to meet those needs (changing stuff, food, drink, toys, whatever). We proved 25 years ago that you cannot work over the seatback from the front, and bringing the infant into the front to attend to needs really doesn't work.
Assuming you're a threesome, and since you're in a 172, plan your loading carefully to avoid running out of aft cg. This may mean strapping a bag into the empty front seat rather than putting it in the baggage area.
Don't bother trying to protect a 3-month-old's ears -- the kid will pull off any headset and pull out any earplugs, and be thoroughly unhappy (and with infants, when they're unhappy, everyone's unhappy) until it's gone. Soon enough, the kid will want his/her own headset (just like Mommy's/Daddy's), but in the meantime, it's like teaching a pig to sing (all it does is annoy the pig and frustrate you).