The US didn't own any of Idaho in 1812, so apart from the silliness of America being reconquered in 1812, this still doesn't work.
I do not expect the capital to be transferred to Moscow, Idaho in 1812 outright. Also, in alternative timeline War of 1812 may simmer for decades (given the British are not decisively defeated in any point). Finally, if not war is not lost in 1812, when? War of 1812 was the only 19th-century US conflict with any European country. Of course, Civil War can still be considered, but i doubt the US government-in-Idaho (Union or Confederate) is plausible from political point of view.
The POD..well, non-extinct and much more vile Rocky Mountain Locust. Well-timed locust infestations can damage the agriculture and economics of the US to the point what conquest by the British may become possible.
Idaho brief timeline (OTL):
1811. First European explorers
1816. British trading posts
1824. US traders arrive
1836. First US settlers arrive
1846. Oregon Treaty - Idaho under firm US control.
Couple a flux of the US refugees from locusts and war-ravaged East Coast to this timeline, and you can get some towns capable of supporting government by 1840 - in the territory which is extremely easy to defend against any potential enemy.