Although a baby which weighs less than 40 pounds can share an adult seat, you may find it more convenient flying with a car seat. Most airlines recommend this, particularly on a long haul flight, for the comfort and safety of both you and your baby. In the United States most car seats will have FAA approval so there certainly should not be a problem with domestic flights. To make sure you are not asked to check your child seat in as baggage you must make sure your CRS is approved and has "This restraint is certified for use in motor vehicles and aircraft" printed on it.
I recommend that you purchase a Jeep Diaper Bag. These bags are big enough to hold spare diapers, clothes and much more besides. The Clam Shell is best as it has a wide mouth opening which provides the easiest access to the extra large main compartment, plus there is usually a changing mat and dirty diaper bag included and pockets for bits and pieces which are big enough to hold bottles of formula etc.
When you have a baby, the first seat you need to buy is the one that is specially designed for babies. These are designed to carry a baby who weighs from 4 pounds to 20 pounds. Usually, they are provided with five point harnesses. Often, these seats are surrounded with foam cushions to provide better safety to your baby. These seats are made to be used as rear facing ones. It is better to leave your baby in a rear facing seat as long as possible. These seats are five times safer than the front facing ones.
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