We took a little trip
Along with Col Jackson down the mighty Mississip
We took a little bacon and we took a little beans
And we met the bloody British in a town called New Orleans.

According to this site http://lsm.crt.state.la.us/cabildo/cab6.htm which appears to be reasonably trustworthy, being a State of Louisiana site, the battle started in 1814 and since the song merely uses 1814 as the year of the trip taken *to the battle site I can see no reason to fault the librettist for historical inaccuracies.