IMO, you should have no problem ASSUMING you can move at a moderate pace. And I'm not even talking about walking fast. However, if you move slow, or need help, or have young kids, or need a wheelchair, or something else out of the ordinary, I'd look for a longer connection.
I think Southwest is only on one concourse, which means you don't need to catch the "Plane Train" between concourses which helps.
One hour is plenty of time for your connection. We've easily made connections there (on Delta) that required us to go from Concourse A to E in an hour with a person in a wheelchair.