If Godwin was discharged honorably after his five years of service in 1818, he would have received three months extra pay, 160 acres of land, and a sixteen dollar bonus. These were the army benefits during the War of 1812. If he lived past 1871 then he and his wife would have qualified for a service pension.
The land would have been in Illinois, Missouri or Arkansas. Most soldiers sold their land warrants to land speculators or to their officers for cash. The land in these states was still in Indian lands until the 1830’s. Very few men settled on the lands which was given to them by the government.
The lands given to the militia after 1855 is another story. These men could receive any government land in any state or territory but they received less than 160 acres of land.
His service record mostly shows that he was present for duty on the dates indicated. He was transferred from the 20th Regiment of US Infantry to the 12th Regiment of US Infantry. Both of these regiments were raised in Virginia. After the war, all of the infantry regiments were downsized and consolidated into eight new infantry regiments. He was transferred to the 8th Regiment of US Infantry after the war.
The only duty indicated in his service record is Belle Fontaine in Missouri which occurred after the war. This was an army post north of St. Louis where the Missouri River enters the Mississippi River.
The service records normally do not show participation in a battle unless the soldier was wounded or had been killed. Then there would be a date to match with a battle.
The 12th and 20th Infantries were in the Battle of La Cole Mill in Lower Canada on 30 March 1814. The 12th Infantry also participated in the Battle of Odelltown, NY (28 June 1814), the Battle of Bladensburg, MD (24 August 1814) and the Battle of Ft. McHenry, MD (13 September 1814). The full regiments did not participate in any of these battles, only detachments.
There would be no way to find if Godwin participated in any of these battles unless you find a family history or it is indicated on a pension (if he lived after 1871).
You are lucky that he served in the US Army. If he had served in the militia, you would not have all of the information about him that is in his army service record. The militia did not keep this kind of information.