Under normal circumstances you should be fine. Usually, early disembarkation can get off as early as 7:30-7:45. Taxis will be waiting and it only takes 10-15 minutes to get to the airport as it's only about 3 miles away. So if all works according to plan, you should be able to get to the airport by 8:30, which is plenty of time.
As for if you miss your flight due to a delay in getting to the airport, if I remember right, Southwest is pretty lenient about it provided you give them notice as soon as possible letting them know you're going to miss your intended flight. This may have changed, so I would suggest contacting SW directly and asking them the question to make sure you get the latest policy.
But to take away all hassle and stress, I also highly recommend you purchase travel insurance. You always hope it's a waste of your money, but if you need it, you're sure damn glad you've got it.