Hi Barb . I think you have found the correct William Kennedy . I Googled --- William Kennedy Loyalist Gaspe --- and the first hit was a Chapter 2 titled Sun Rises In Our Parish 1783 Arrival Of The Loyalists , which mentions this said William Kennedy and his large family at Gaspe Basin Douglastown Quebec .
I also found a William Kennedy on the Old United Empire Loyalist List , but he was listed at Saint John New Brunswick , could be a different man , or he may have chosen to relocate to Quebec .