Good response from Lindsey. In addition to what she advised, you can also gate check your stroller for free so that you get it back at the jet bridge upon arrival. It's free too, so that does not count toward what you checked in for collection at baggage claim.
At boarding time listen for the announcement for family boarding (between the A and B groups) so you can board the plane while there is still plenty of free seating.
I suggest picking a seat near the back of the plane so you are close to the aft lavatory. This way you can change junior there without a trip all the way up to the front, where you are not allowed to form a line to wait for it to become available. At the back, you can hang out there without restrictions. One year olds (especially boys) can get ansy and it's nice to be able to let them stand up a bit during flight while you're still close to your stuff at your seats.
Also be sure you have something for your son to drink. Maybe if he still uses a bottle at all, that woudl be a good way for him to clear his ears, which can be a problem at that age, as he might not know how to do it yet. I always carry candy with me as well as a tool to distract what might otherwise be a miserable kid.
Finally, recognize that there is no video entertainment on SWA, besides what you bring with you. You can use their wifi to watch TV, but wifi does not always work on all flights. As long as you bring plenty of activities to keep your little guy busy the whole time, and whatever he needs to sleep, you should be in good shape.
