Bandon in County Cork (where one Margaret O'Brien was baptised in 1819) is 123km from Caherelly in County Limerick (where the other Margaret O'Brien lived at the time of her marriage in 1836):
https://goo.gl/maps/JDhMVBKBqAbM7SPVA
That sort of internal migration in rural Ireland would have been extremely unusual at that time.
Margaret O'Brien is a very common name. By 1911 (by when the population was much smaller, but the survival rate of records is much higher), there were 919 Margaret O'Briens in Ireland, not allowing for any spelling variations:
http://www.census.nationalarchives.ie/search/results.jsp?searchMoreVisible=false&census_year=1911&surname=o%27brien&firstname=margaret&search=Search
By comparison, there were only 289 Dan* H*r*g*ns, and the wild cards pick up completely different names such as Harrington and Hartigan as well as numerous variants of Hourigan (but not including Organ).
Old Age Pensions were not introduced until 1909. Before then, pensioners were almost exclusively military pensioners. Police pensioners tended to explicitly indicate that as the source of their pension.
The use of the various extracts at familysearch.org and elsewhere from the Irish records freely available online at civilrecords.irishgenealogy.ie, registers.nli.ie, etc., should be discouraged as the extracts often miss critical details from the originals.
Given the patchy survival of records and the limited internal migration, you should start with the place where you know your ancestor lived and concentrate on the surviving records for that place, rather than hop around the country looking for other people with similar names living in places with a better survival of records.
A good source for identifying which records survive for a particular place is
https://www.johngrenham.com/browse/