As commented the Irish Catholic Parish Registers images are on the NLI site as images only.
The microfilm images were jointly transcribed by Ancestry and Findmypast and appear on both their sites.
BMB are all lumped together by Ancestry but split on FindMyPast and searching specific counties and places or specifying mothers and fathers is easy there. Entirely free to search and view on FindMyPast only have to register/create an account not take out a subscription.
https://search.findmypast.com/search-world-records/ireland-roman-catholic-parish-baptismsMany of the early Catholic parish registers are in a poor state and legibility can be an issue.
RootsIreland consists of a group of county or area subsites and genealogy centres working more locally. Their index only collection is from the original registers not from the microfilm so there are differences.
Findmypast search produces no Rose Doherty+sounds like or looking inputting D*h*ty in Co. Donegal 1833 ±5 no forname. That is perhaps understandable as only Clonleigh Parish in the entire County has RC registers going back that far and when you look on NLI map and open that parish whilst registers start 1773 is 1773-95, 1836-7 then a run from 1853. Culdaff starts 1838.
Rootsireland coverage table for Donegal with start dates
https://rootsireland.ie/donegal/online-sources.phpJohn Grenham's
https://www.johngrenham.com/records/county_church_full.php?county=Donegal&search_type=full&denomination=Roman%20CatholicSo, like you, not having a current sub to RootsIreland I do see inputting the name produces 6 results, they could be Church of Ireland, Presbyterian or Methodist. So what church did she attend/marry in subsequently? If she was you suspect RC then your not going to find her.