The first events are right. However, Key wrote the "Defense of Fort McHenry" in 1812. It was later published and finally published as "The Star Spangled Banner" in 1815.
http://www.contemplator.com/america/ssbanner.html
Please check:
1812- United States declares war against Britain
The warship Constitution defeats the British ship Guerriere
1813- Battle of Lake Erie
Battle of THames
1814- British burned Washington, D.C
Battle of New Orleans
1815- Francis Scott Key writes "The Defense of Fort McHenry"
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