I had to travel on family emergencies twice recently, and Southwest made it easy both times. On both trips my 15 month old baby girl came with us. On all four flights, we didn't buy a ticket but the ticketing and gate agents dutifully checked to see if there were available seats on the flight for us to install the car seat. And flight attendants didn't make us feel like thieves for installing the seat in a space we hadn't paid for.