The 20 month old will be able to sit in your lap, any child under 2 can do this. I always purchased a seat for my son when I started flying with both him and my daughter who is 2 yrs older. It made it so much easier to take the car seat on the plane and have my hands free a lot of the time. I know now though there are more restrictions to which car seats you can take on planes. If you are doing this check with the airline.
Bring lots of snacks and toys that won't easily roll away like anything that is round (crayons) or has wheels (matchbox cars). When they drop they roll several isles away and can be difficult to retrieve.
Good luck!!
