I traveled a TON on southwest before my son was a year old - cross country from CA to PA and some from CA/PA/TX. Make sure your car seat is FAA approved, and bring it to the gate to check in - it will travel safer that way. PLUS, if the plane is NOT full, you can bring it on and strap your little one into the carseat in the open seat. I was able to do that on a couple of flights. Make sure you do the checkin 24 hours in advance to get the best checkin number you can.
Also, if the plane is not full and you sit with your hubby and a baby, 99% of people will chose to sit away from a baby.
Be prepared to BF on the plane if you want to. I was almost exclusively BFing when I traveled. I sat in the window seat so I always had privacy on one side, and if your hubby is sitting with you, you'll have privacy on both sides, so no issues there. No one else will be able to see you.
Take a few favorite toys - don't go crazy. There are diaper tables in the bathroom, I believe - they fold down from the wall above the toilet. You can also give Southwest a call and talk to them about traveling with an infant. They're very nice.
I traveled ALONE with an infant several times. The lifesaver for me was my ERGO baby carrier cause I was able to strap my son on my back and then carry, pull, etc. whatever I needed onto the plane. I also used a go-kidz travelmate to put wheels on my carseat since I knew I'd be traveling with it and needing the carseat. It was great. Perhaps one of those portable luggage carriers and those bungee things to attach the seat so you can roll it around easier.
Feel free to contact me directly to pick my brain for more info :)