You're doing the right thing. I suspect the airlines don't challenge parents on domestic flights because they have no way of verifying anything. If they start asking people to carry their kids' birth certificates, you know half the parents will forget- either through an honest mistake in the rush of getting to the airport, or because the child is over 2 years old.

The best-behaved small children I've seen on planes have been the ones with their own seat- preferably a familiar (FAA-approved) car seat. The worst have been oversized lap children- and it's got to be miserable for the parents, too.