I would suggest leaving the car seat at home, or check it if you need it in a car at the destination. I bolded "car" because it's called a "car seat" for a reason -- it is designed to withstand the forces of a car crash. It is not designed to withstand the forces of an airplane crash; well, considering the forces involved, nothing will, although a seat belt might come in handy.
An 18 month old in a seat by himself with a seat belt will be perfectly fine. Heck, you could hold the child and still have a 99.99999999% chance of surviving, but the separate seat may be more comfortable and provide a 99.999999995% chance of survival. ^