Check everything: your car seat*, stroller base (make sure you get a travel bag for it) and bags. Make sure your diaper bag & your purse are your twp allotted carry on items.
*if you have purchased a seat for baby, you are welcome to bring the carseat onboard. Most fit perfectly into the regulation airplane seat. Sometimes, if you are lucky, an open seat is available and a flight attendant will let you have that open seat for baby. In this case, you might be allowed to also free to bring that car seat on board. Check with the attendant. In this case, they are your best friend.