Are you sure of the name and time? Many pre Civil War militia companies used Washington in their name. Some famous units are The Washington Grays of New York, Washington Light Artillery of Louisiana and Washington Light Infantry of South Carolina. I specialize in Michigan and there was in 1861 a Washington Light Artillery in St. Clair Michigan which likely changed its name to Washington Guards when joining the Mich 5th Inf Regt. Many other states likely had companies with “Washington” names; if you could give a state it might help you get an answer.
To Join the Company of Military Historians click here