If Madison holds off a year, there probably isn't a war. The Orders in Council are abolished and America loses a huge plank for its war effort. The vote for war was very narrow in OTL even with the Orders in Council. You've also got Napoleon and his failure in Russia with Britain and her continental allies on the upswing. The window for war was extremely narrow.
Frankly there's where the timeline is in this WI. Madison selects Moreau as SoW, Secretary Moreau takes one look at the pathetic state of the US military, and about has a fit. He argues endlessly with Madison about this, and while he fails to get the military he knows that he needs he does manage to get Madison to delay any war with the UK. By 1813 the casus beli is gone, and the war is averted. Moreau has implemented some reforms and improved the management and integration of militias, but the US is still not truly ready for a major war, and will be more likely to know it. Madison is a small government antifederalist with a disdain for standing militaries, but much more pragmatic than Jefferson, and may be willing to take a hard look at the US military, as might whomever takes over after him (Monroe?).
However, IIRC many of the underlying issues that the war partly sorted out, e.g. the borders, the status of New Orleans, British support for indigenous war efforts, etc., are still there to cause ongoing tensions.
Someone could conceivably make a TL from this PoD where the War of 1812 is averted, but another Anglo-American war, perhaps over Oregon or NOLA or Indian wars or something, does happen. Hardly my area of expertise on what happens next, but I'd be interested in seeing what unfolds if somebody went there.