I don't think you'll have too much luck finding her unless you have much more specific information. You will be relying on church records & at present only the records for north & east Cork are available online on
www.irishroots.ie. A search of these records for Catherine Leary born between 1802 & 1812 show 9 available records in this area alone.
There are no available records for travel between Ireland & England in the 1800s.
If she was a widow when sent to Australia was Leary her married name? If so you need to find marriage record to get her own name in order to trace birth. Did she marry in Ireland or England?