This should be doable, but I would make 100% certain that you are on a single ticket. If you are on separate tickets and miss your xIAD, you may or may not be rebooked. Aircraft are late and there are traffic accidents and the like. It's a lot to risk.

Some carriers will take pity and rebook you. Others (and depending on the fare basis on which you are traveling) will either require you to buy a new ticket at walk-up fares, charge you the fare difference or require a change fees.

Taxi from DCA-IAD should be easy on a Saturday PM. Presuming no checked luggage, just walk out of the terminal, there will be a taxi line to your right and that line moves quickly. About 45 mins to IAD should get you to IAD at T-90. That's fine on a Saturday PM.

You don't provide the carrier xIAD, but carefully read the check-in requirements for that carrier. Make certain that you meet the deadlines for check-in (including passport & document check by the carrier) as well as gate times. Remember, if you are required to be checked in with docs reviewed no later than T-60, that's 8:45 PM, not 9:45 PM.