@jacobsmom, try to not have a carry one on then. Just the diaper bag for baby because it would be crazy to handle diaper bag, baby and carry on.
I took late flights so he would sleep. I think he was 4mo when we flew
Baby wear in the airport, breastfeed/bottle during take off (and landing if awake) to help keep his ears from popping.
Try to book your flight during the time you know they will nap! That really helped me. Are you traveling with someone else?