There is an excellent set of records if you are looking for ancestors in the challenging time period for Canadian Ships Passenger Lists before 1865.
These Irish passenger lists from shipping records can be found ONLINE in
Passenger Books of J & J Cooke, Shipping Agents Sailings from Londonderry to Philadelphia Pennsylvania, Quebec, St. John New Brunswick & New Orleans Louisiana, 1847-1871 in Reference D.2892/1/1-14 (see also MIC.13 in the Public Record Office of Northern Ireland)
These records are FREE and have been transcribed by a team of Olive Tree Genealogy volunteers