Hi J.R. The Col. Williams you are looking for may come from the same extended family, but he is not the same guy. The Col. William Williams that I started this thread about turns out to have been William IV. He was born in 1736/37 in Boston, married Zilpah Wilder, moved to Vermont in 1769, was a Colonel in the American Revolution, and then moved to Quebec around 1805. He died there in 1822. So he would not have been in the War of 1812.
His father was also Col. William Williams, but William III lived 1711-1785 so he would not have been in the War of 1812 either.
There was a William V, 1782-1862, but he went to Quebec with his father, and later moved to Ohio. I did not find any reference to him being in the military.
Sorry I can't help you!
Dotty