Airlines do recommend that you bring a car seat or some type of child restraining device for small children. However booster seats are not Federal Aviation Administration (FAA) approved and are not permitted to be used onboard an aircraft. Airplane seat belts aren’t designed to hold two year olds very well. The FAA recommends using a CRS. A CRS is a hard-backed child safety seat that is approved by the government for use in both motor vehicles and aircraft.
This is a great resource for child safety on airplanes: fly children.