Welcome to Ireland Reaching Out!
Have you already had a look on rootsireland.ie for any records of the family?
As with most emigration programmes, adopted countries were more concerned with who was entering their their country that the British authorities were in recording who was leaving Ireland. This is why it will be the adopted country that will hold the information, like Castle Garden/Ellis Island in the US, for example. For Canada Library and Archives CAnada will provide further information