Specifically looking for information on what the average Soldier was like during the War of 1812 (age, size, et cetera). Can anyone point me in the direction of a book or another resource? Or if you have any insight into this, that’d be great too. Any help is very much appreciated.
I'm afraid you are going to have difficulty getting such information, except for the 1812 discharge Certificates recommended by gps93. The Army simply did not begin collecting such data until much later than 1812. One source you may find useful, however, is the publication by Edward Cutbush on preserving the health of soldiers and sailors about your time period (1808). Although he was a Navy Surgeon, he provided a large section devoted to the Army and physical standards. He noted that "In raising an Army, attention is necessary to procure men who are free from disease and capable of undergoing the fatigues inseparable from a military life". He discussed the desired ages of soldiers, and the preferred sizes of soldiers for various categories of service-- this should give you a general feel for what sized soldiers were potentially available. This reference is: Cutbush, Edward: Observations on the Means of Preserving the Health of Soldiers and Sailors: and on the Duties of the Medical Departments of the Army and Navy: With Remarks On Hospitals and Their Internal Arrangements. Pub Fry and Cammerer, Philadelphia, 1808. Otherwise, it is very hard to generalize-- most soldiers in the War of 1812 were locally-procured militia, and all physical standards (including age and size) were widely variable.
Since you don't specify which army, I'd recommend the following book. It will provide you with the details you're asking about for the British army of the time.
"All for the King's Shilling: The British Soldier under Wellington, 1808–1814" by Edward J. Coss.