I'm doing the same thing next month. You can hold a child under 2 years on your lap for free, they said you just have to being a copy of birth certificate and go to the ticket counter before the flight to get a pass for your baby. For Southwest you can also being a stroller for free along with your 2 free checked bags. I think a car seat will count as a checked bag though. We are renting a car seat at our destination so I don't know about that. Hopefully it will go well for you, I'm hoping my son will be good for us... haha.