Most of the airlines with a flight of that long are going to have a layover somewhere. I checked two of the airlines and neither offers a direct flight from Reno or Las Vegas ( not sure where OP flies out of) To Atlanta.I have an ex-SD who's 4'8" - full grown - and perfectly healthy.
Most airlines won't let a kid take a connecting flight until they're 8 (or older on some airlines as acmb pointed out). All we know is that the child is 7 now, we don't know if he'll be 8 before the next need to fly comes up. We also don't know if a connection is needed between the two cities.
But it really doesn't matter. If the court orders Mom to get the child to Dad (or vice versa), and they're unwilling or unable to let the child go unattended, then they'd better go on the flight with the child - or face contempt.
I then called my sister who works for Continental and was told that a nonstop flight between those cities would be very hard to find with any airline and if you do there will be very specific times they are available.