It’s only about 30 min. from port to airport.
The port is attached to the Riverwalk, which is a long mall facing the Mississippi River. It has some touristy stuff in it. Candy stores, fudge making, toys, etc.
At the other end of Riverwalk is the Audubon Aquarium, which is a nice way to kill a few hours. Not sure what you’d do with your luggage in the interim. The Aquarium *might* have a coat- or baggage-check, but definitely call ahead to confirm if you want to go that route.
There is nothing to do around the airport. If you have Delta SkyClub access or PriorityPass, those are open and they are nice lounges, but there’s nothing in the airport particularly toddler-friendly.