At Enotachopo Creek in 1814, the American forces were ambushed by Red Stick Creek. While the advance guard kept to their orders and counterattacked, the rear guard panicked. However, the Red Sticks did not take proper advantage of this, and were driven off. But let us suppose that this did not happen. Instead, they manage to strike decisively against Jackson's mostly inexperienced men. During the fighting, a bullet strikes the Major General, who dies face-down in the muddy water. As his forces retreat, the Red Sticks might even be able to capture a few pieces of American artillery.
It is, of course, implausible to think that this would help the Red Sticks win the war. The 39th infantry was already on its way to Fort Strother, providing reinforcements against the Red Sticks. However, I'm interested in whether the war will be prolonged, how this might affect the War of 1812, and what the final results of the war might be (the Treaty of Fort Coffee? Fort Cocke?).
(This can, by the way, be seen as a sneakier way of doing the classic "what if the British win at New Orleans": it involves Jackson eliminated and a potentially weaker position for America in the South, but starts of before the Treaty of Ghent)