I searched the free site www.irishgenealogy.ie for a civil marriage record for Andrew and Rose but did not find the marriage. Possibly they were not married in Ireland or they did not civilly register the marriage. Also, if they were married in Northern Ireland, a record would not be on www.irishgenealogy.ie but on the PRONI ( Public Records Office for Northern Ireland).
Farrell would not be a Donegal surname but McLaughlin/McLoughlin is very common.
We only have access to images of civil birth records up thru 1920 because of Irish privacy rules. I did check the free site familysearch.org and saw index records for births for your father and siblings in the 1930s/early 1940s. It looks like the marriage between Andrew and Rose was around 1930.
I looked for civil birth records for Rose McLaughlin between 1911-1920 in the Inishowen registration district and there were 20 Rose McLaughlin records. Likely your grandmother was one of the 20.
Any other clues on your family?
This Facebook group may be of interest https://www.facebook.com/ClonmanyGenealogyPage