If Michael Tinney was in the county in 1812, at the age of 16 he would have been required to muster for militia service during the War of 1812. The Prince Edward Militia rolls from the War of 1812 are online but not all of the papers would have survived the last 200 years. A search of the rolls would take at 1 to 4 hours depending on how many pages there are for that regiment. I have an index. Please let me know if you want to take on this search.
Quakers had an exemption from bearing arms but not militia service. However, many refused to muster and may have had to pay penalties. The Quaker response to the war was mixed. Some served as officers.