There was indeed a Martin Gouge who served during the war of 1812, but something is clearly off here: Martin did not serve at age 6. Either the birth date is very incorrect or this honor belong to a different profile.
Also, the Martin Gouge who fought in the war moved to Missouri sometime between 1815 and 1818 -- with two sons. This Martin Gouge would have been ten years old, and unlikely to have multiple children.