Saturday and Sunday mornings are horrible at Dulles. Twice we have arrived 2 hours early and barely made our flight. Security lines are very long and just a tip, go to the security line from the right side of the terminal (it is more towards the middle by the employee security checkpoint) Don't get in the line by United Airlines, everyone seems to use that one. The one on the right moves much faster because there are fewer people. Another tip is to wear slip off shoes and not tie shoes, yes you do have to take them off, and put all your keys, change, cell phone, etc. in your carryon as this is also faster. I would plan on being there by 9:30 or so to ensure you have enough time to get through security and grab something to eat. Better to be at the airport without feeling rushed with a toddler than feeling rushed and risk not making the flight.