Have you marriage and death certs for your John ?
You generally require a bit more detail to start a search for early records like this - e.g. his approximate year of birth, some family details (parents are included on certain Australian certs), and usually also require a more detailed place of birth, i.e. the name of the town, townland or parish this [O']Mara family lived.
Note the O' prefix on surnames could be added or dropped at various times. Also bear in mind that the surname may be spelt [O']Meara
see :
Introduction to Irish Records My Ancestor came from Ireland - where do I start? There seems to be two references to your John on the
Ireland Australia Transportation database at the National Archives of Ireland. This is a finding aid for the few Transportation details that have survived in Ireland. These documents only cover limited dates, and generally these relate to appeals etc.
1. Name : John Mara
Age: 20 (so born c1830)
Trial location : Longford
Trial date: 30 Dec 1850
Crime : Burglary
Sentence: Transportation 10 years
Document Ref: TR 11, p 112.
2. Name : John Mara
Age: 20
Trial place: Longford
Trial date: 30 Dec 1850
Crime : Burglary
Sentence: Transportation 10 years
Ship: Phobe Dunbar
Document Ref: TR 10, p 177.
There should be at least some details surviving for the references mentioned - although these might just be a mention of this John on a list. The documents are not online and are held by the National Archives in Dublin, so a visit by yourself or a researcher would be required to access these.
Shane