Anne was baptized on the 18 Oct 1876, but that doesn’t fit with the civil register entry, which lists her birth date as 19 Nov 1876. I think we can all agree that it’s impossible to be baptized before one’s birth, so we have some ‘splaining to do.
What I think must have happened is that she was born in October, but the birth was registered late (6 Dec 1876). That lapse in time was either by chance or design. Possibly the mother, who registered the birth, forgot the date, or she could have deliberately given an incorrect date. This sometimes happened when a family did not have enough money to pay the birth registration fee. The registration was put off, until the funds were acquired, and then the birth was registered with a fudged, later date, in order to prevent paying a late registration fine.
We can never know what exactly happened, but I find it more likely that the delayed registration is incorrect than that the Church got the baptismal date incorrect.
In cases like this, where there is a conflict between an earlier baptismal date and a later birth date, I think it’s best to use the baptism date as a birth date. In this part of Ireland, at this time, folks baptized their children pretty soon after birth, so I feel this is a reasonable solution to the problem.