Documents held by the Library of Congress are made available at this site. These papers include extensive correspondence and notes pertaining to the War of 1812. The site offers digital images only—no transcripts.
The Avalon Project at Yale Law School hosts a site dedicated the documents of the War of 1812. It included texts of the United States declaration of war, the Treaty of Ghent, and miscellaneous public documents pertaining to the war.
"Selected Works of James Madison" are available at this site sponsored by the Constitution Society.