As others have said, you have plenty of time for public transportation. Uber is a good option but will be fairly expensive compared to the alternatives and may not even be quicker since it will be rush hour and 66 gets pretty backed up going east into Arlington every night.

I've taken public transportation from IAD to DCA. As catocony said, the way to do this is to take the Washington Flyer from the terminal to Wiehle-Reston, then the Silver Line to Rosslyn and the Blue line to DCA from there. It'll probably take about an hour door to door during rush hour, maybe an hour and a half.