My research shows that most of the Irish of the 1800's left Ireland via a special purpose emigration port set up in Queensland (later changed to Cobh)in County Cork. The typical sailing route was from there to a stop in Liverpool, England and then on to destinations across the Atlantic.The folks arrived to the Queensland port from throughout Ireland by train. Don't think many left via Dublin. The port of Dublin was used for incoming passengers and freight operations.
Google 1821 Census of Ireland and you will find numerous hits to start your search.Jim