People were using rockets in 1812…..?
Yes, and even before. You'd be surprised, the things you can do with enough gunpowder. More can be said on the matter of rockets, if anyone else would like to show their knowledge of 1800s-era ordnance; for the meantime, OP, these previous threads may be of interest to you:
Rockets have been used in war at least going back to the 13th century, but they were more heavily used in Asia earlier on.
Both China and Korea made use of carts holding racks of many rocket propelled fire arrows (Huo Che (Chinese) or Hwacha (Korean)) which could be used both on land or at sea. Mostly these were defensive weapons since they could deploy a devastating rain of arrows in a short period of time, but they could not be used to maintain fire for a long period so they were rarely used offensively. These inventions were also adopted by others in Eurasia including the Mongols (who spread the technology to many areas they conquered), parts of the middle east, India, and even parts of Europe.
Over time the simple rocket propelled fire arrow had evolved into a stick rocket that had a small explosive warhead (a powder charge which has a fuse ignited in series with the propellant charge). These are, of course, very similar to fireworks rockets in that they propel themselves a significant distance (up to hundreds of meters) before they explode. In the case of display fireworks this explosion is intended to happen in the air and be optimized primarily for sound and visual display. Whereas military rockets would propel the warhead on a ballistic arc toward an enemy where the explosion would be designed to cause damage.
By the late 18th century the Kingdom of Mysore in Southern India had advanced the state of the art of such military rockets to the point where they had become particularly devastating. They scaled up such rockets to be closer to spear sized and instead of using just wood or paper as a casing for the rocket and the warhead they began to use iron. This gave them greater range and allowed the rockets to be much heavier and more damaging (though timing the fusing right on such bombardment weapons would remain a pesky difficulty until the mid 20th century). When the British encountered such weapons used against them to devastating effect in the various Anglo-Mysore Wars of the late 1700s they were keen on copying the technology.
William Congreve adapted the design of Mysorean rockets in order to build much heavier and longer range rockets for the British military. Congreve rockets ranged in size from about 6 up to 42 pounds with the ability to propel a payload of canister shot, a simple projectile shell, or explosives to distances as much as 3000 yards. Larger designs existed as well, up to 300 pounds, but those were too unwieldy for practical use. Such rockets had low accuracy but they made up for it with a very high rate of fire, making it possible to deliver thousands of rounds in rapid volleys lasting just tens of minutes.
Congreve rockets were used by British forces throughout much of the 19th century and were used notably in the Napoleonic Wars and, of course, in the War of 1812 where their use was immortalized in the form of verse which has since become the national anthem of the United States of America. They were obsoleted by the development of more modern rockets (which removed the need for the use of a guide stick) in the mid 19th century as well as by massive advancements in the development of high precision artillery not long after that.