Presuming these might be Catholic families?
The catholic parish registers are now online, free of charge!!
registers.nli.ie
You could try looking in there for his baptism in 1881 if the records are available, some of the parishes don't include records that late on, but worth a look. The site if fairly easy to work out.
Considering you have his birthdate, and an area, in theory it should be relatively easy to find his birth registration. This will of course give you a bit more to start researching. Again, you have his parents names already (from his death certificate perhaps??) so it should be easy enough to find their marriage registration. You might also find this in the parish registers with some methodical searching through parishes in the Cashel area.
As for his immigration to Australia - do you know what state he ended up in, as you may well be able to find more on his immigration online. NSW State records has excellent immigration records on their website for free.
