All true, I put the issue in 1819 just to avoid too much future gazing.
Hmm, well Jackson could have been explosive enough to spark a war. Wonder how Jackson (being older) would fare in a war time environment. He would probably never run for president.
Jackson might not amount to anything without his victory at New Orleans to propel him to fame and glory. He'll still be the champion of an Indian war, but without the greatest victory in American history (thus far) his star will never shine as bright. He made so many enemies throughout his career that without his great game I think someone will bury him in an election if he goes for the presidency. Adams hated him, Crawford hated him, Clay wasn't a fan.
One thing in 1819 would be Spain's position in Florida. Britain had been fooling around there for years until New Orleans smashed all of their intrigue on the Gulf Coast permanently. I can see them being very active 1812-19 in a peace scenario.
In OTL Monroe and Crawford (the top two contenders for the 1816 election) were both very pro war, but much of that had to do with the Orders in Council. I'm not sure either would be willing to declare war without something that big in the background.