It was normal for the Poor Law Union to look after it’s own residents. In other words if Mary Kelly was in Letterkenny Poor Law Union, there’s a high probability she had lived there for many years and was probably born in that area.
The problem you face in tracing Mary’s birth is that very few RC parishes in Co Donegal have any records for the 1820s. The parish around Letterkenny is Conwal and its records don’t start till 1853, so the chances of finding a record of her birth are pretty low.
Here’s some information on Letterkenny workhouse.
https://www.workhouses.org.uk/Letterkenny/From this source it looks as though the admission records pre 1864 have not survived. They do have the Board of Guardians minutes from 1841 onwards. The Board of Guardians met weekly and their minutes contain the normal sort of details you might expect to find in any organisation ie approval of expenditure on food, wages, repairs etc, dealing with management issues, analyzing the numbers in the workhouse (and on outdoor relief), the numbers in the hospital, general health issues etc. Occasionally inmates are mentioned by name – often if they did something notable eg fighting or coming home drunk, if allowed out for the day – but mostly it’s focused on the management aspects rather than the details of each individual resident. I couldn’t rule out that you might find a list of those selected for one of the emigration programmes, but it might equally just say: “X number were selected for Australia and are to depart on Y date.”
I looked for deaths with the surname Hetty in the Letterkenny area 1864 – 1901 but did not find any at all. There isn’t anyone in Ireland in 1901 with the surname Hetty so I suspect that may have got garbled over the years. Not sure what the correct version might be. (Could it be Kelly mistranscribed?).
