Check out Wolf Trap Artsplay in Vienna.
I also am fairly certain that Kindermusik offers classes in Reston on the weekends - they have severely limited their Ashburn sessions.
When she is older, Reston Conservatory has Baby Ballerinas weekend sessions.
Also look at Fair Oaks, Reston, and Loudoun Hospital. I took an infant massage class in Fair Oaks when my first daughter was smaller. At that age, it is a great way to build intimacy with your daughter. Ina few months she will enjoy the music/gym classes a lot more.
Congrats - I too have a four month old in Ashburn! Enjoy every minute. I think it is easy to miss out on some of this fun stuff when you work full time, so it is great you are trying to find something. I think you will have fun. Be persistent. (I worked full time eith my first child for the first year)