I am a former SWA flight attendant...don't stress about this. If the flight appears to be full, they will inform you that your dd needs to sit on your lap during the flight. If the flight is fairly empty, they will usually let you know this as well, so you can plan to have a seat for your dd as well.
I usually asked parents to go ahead and take an extra seat, and I would let them know later if we were going to need to take it.
Just an fyi...traveling with a nearly 2 yr old on your lap can be very uncomfortable. Also, FAA regulations will not allow her to be fastened in with you during take off and landing (it is very dangerous), so you will be fastened in, and she will be held in your arms. There is NO way you could safely hold her during a crash, so these children are at a much higher risk of injury/death if the plane were to be involved in an accident. The FAA is considering disallowing any "lap children" in flight. I am not trying to stress you...just tell you the facts. Planes have VERY few accidents, and SWA is a VERY safe airline.
Please remember to bring your birth certificate with you, as you will have to show that she is under 2 for her to get on free, and do NOT check your carseat until you get to the gate. If there is an available seat, she will be MUCH safer in the carseat. If there are no available seats for her, the ops agent can check the carseat for you as you board.
Beca