You are in the wrong branch of the hobby. The war of 1812 has nothing to do with figures based in 16th century, nor with the Warhammer universe. Not historically, not militarily, not esthetically.
So what? I saw a mini feature on a WWI themed Imperial Guard army in White Dwarf a little while back.
If I were looking at doing a Vietnam themed army in Fantasy, well, that wouldn't really work. But the fighting style back then was really quite similar to that of the actual gameplay of Warhammer. Regiments, cannons and such.
I read somewhere that basically two opposing forces would line up across from eachother and shoot eachother in an agreed upon manner.

I wanna play Warhammer and the only place that I really know of is Games Workshop. In order to play there, they need to be Games Workshop models. Nuff said.
I don't know any Historical places nor is there an apparently decently sized community. What appears to be the official website looks like something anybody hastily put up.
Aaand, when you play historical, everyone's seen a British Napoleonic era force. I haven't yet seen a Warhammer army themed this way. There probably is. It's about time for another.

Just a short while until I get that box of handgunners and then I'll find out if it's really that hard. I can find other ways.
I just finished converting my sixth bike for my Space Marine biker army (check out the progress
here)and I've got to say that this looks pretty easy. Meticulous, but easy.
At the moment it looks like what I have to do is file off the poofy bits (where applicable), fill any necessary spaces with green stuff, add little tails and finally make shakos.
Voyageurs are even easier. Just pretty much leave them as is, making the odd headwear change.
I'm looking at this not so much as an Empire army but rather my own army with Empire rules. These aren't your standard guys from Ostland.

But the way I see it is that I have a certain set of guidelines to follow and then from there I can do just about anything.
And if it gets really sticky I can add lots of spearmen and call them handgunners who've run out of ammo.
But just picture it:
"In this corner: A slithering Slaanesh army!
Aaaaaaand in this corner, their challenger is...The British Army!"And I love going to fort York and checking stuff out there.
I "worked" there one summer as a drummer. Maaaan those uniforms are not fun to wear.