Hi Noeleen
I haven't got the sites at my fingertips but drag through the Australian Board on Rootschat as I'm sure so many having been using useful sites and you may see what you want there.
After that, if nothing turns up then post a query. The Arrivals are well documented for those we have searched for. Where are you - in UK or Australia as the Australian Papers had a wonderful Shipping News column which so often, as you have a small time frame to search, gave passenger names, admittedly sometimes Steerage were all lumped together.
I'm no expert but I would be sure to say that most Irish left from Liverpool as I know my Isle of Man immigrants went there to get a ship. Unless there was some reason to be in London and leave from there.
Good Luck - Faith