This is probably not the same person becaue this is a much later war, but, from "Military History, Wayne County NY" by Lewis H. Clark, pub. Sodus NY 1863: War of 1812 39th Infantry, Company of Capt. John Holcomb Jan 16, 1813 to June 24, 1813 and to Dec 25, 1813 Fifer (sic): JOEL DOOLITTLE Drummer:Asher Doolittle
Wayne County was not yet established in 1812. It had earlier county designations and divisions as Montgomery, Herkimer, Onondaga, Cayuga, Seneca etc. I'm not sure of all the dates and complications of this. But much of this area was settled by Revolutionary War vets who were granted land here (military tract). Is it possible that Joel and Asher Doolittle's parent was one of those?