The most important hero of the War of 1812 was Andrew Jackson. His leadership was important for the war effort because it was instrumental in winning the Battle of New Orleans. This win helped push Jackson to national prominence, helping him to eventually become president of the US.
Although the Battle of New Orleans happened after a peace treaty had been signed (the armies were unaware of this), it was still very important. If the British had won and had taken control of New Orleans, they could well have exerted a great deal of pressure on the US regardless of the peace treaty. This was true because New Orleans was the most important port for the entire Midwest since goods came down the Mississippi in this pre-railroad and pre-canal time.
By winning this battle, Jackson kept this from happening. For this reason, he was the single most important hero for the US in this war.