Notes On The Ohio Militia during the War of 1812 by James T. Brenner, included:
"The military policy of the United States during the post-Revolutionary period relied upon a small national army and a robust state militia force.."
More about the militia from the University of Dayton website:
Following the war, the United States reduced its standing army to only a handful of men, entrusting the state militias with the nation's defense.
The Anti-Federalists opposed federal control of the militia for three reasons. [See Fear Of A Standing Army]
The Constitution's drafters hoped that the militia would remain the nation's primary means of defense against foreign aggression. Considering the development of military tactics and technology of the time, the state militias were able to adequately fill this role.
Specific action for the Ohio Militia in the War of 1812: