Yep, Mr Murphy is correct! There are some pension applications still surviving.
The old age pension was introduced in January 1909. To qualify, anyone who claimed had to 'prove' their age and this was done by checking the 1841 and 1851 census returns, which still survived at that time. So if, for example, Annie Doyle claimed she was 75 in 1910, she would make a 'green form' claim stating where she was living during the time of those censuses, and with whom. The pension bods would then check her details and would expect to find her recorded in one or both of the early census returns.
Some of these 'green forms', annotated with the civil servants' finding, have survived and can be studied at the National Archives in Dublin. If the claimant was 'found', a full transcription of the household's census record was added or attached to the green form. (I'm not sure what proportion of the early 'green forms' survive.)
As far as I'm aware, the only online source of these pension claims is
www.pensear.org. Charge £2 a view.
Rose