Washington Flyer has a monopoly on taxi service out of IAD. Other taxi companies can take you TO Dulles, but they are the only ones that can take you FROM Dulles. I have no idea about the availability of infant seats, but here's their website and maybe you can contact them directly with your question:
www.washfly.com/Taxi.html
Another option is Super Shuttle:
www.washfly.com/super_shuttle.htm
The bus/train connections are certainly cheaper, but a bit more hassle, especially with a baby in tow. You can take the Washington Flyer coach service to the West Falls Church metro station and take the subway in from there. Or you can take Metrobus 5A to the Rosslyn Station and take the Metro Blue Line from there.
The Smithsonian Air & Space Museum is certainly a must, and I'd recommend the Natural History and American History Museums as well. A couple of other interesting spots are the Newseum (
www.newseum.org) and the International Spy Museum (
www.spymuseum.org). Both of these require paid tickets though.