I wonder if Mary was a twin ? I notice that NSW BDM Early Church Records have a baptism for a Charles GRIFFIN with parents as Patrick and Bridget. It is Volume 63, line 1475 and according to the NSW BDM it drills down to 22 January 1843. Of course, being a baptism 22 Jan 1843 may well be the date Charles was baptised, rather than his date of birth…. Mary’s baptism is 1843, Vol 121A, line 862. I have not found a second entry in the online index, so I cannot confirm if either of those two baptismal records are the transmitted registration or the original parish registers’ entries.
Civil registration commences in NSW in March 1856. And it is not at all unusual for the NSW BDM’s ECRs to not include all the burials (or the baptisms or the marriages). Once you know the denomination and its respective parish for the family at any given year in the mid pre 1856 decades, then you can start to strive for the likely cemetery, and/or the church register. But do bear in mind that the church registers are not public property. The churches are usually co-operative, and quite often refer you to the Diocese and their private archives. Patience is needed and a gentle polite approach is likely the best way

and of course, snail mail with a copy of the NSW BDM records that prompt the enquiry can be very helpful to the volunteer who may be the one to carry out the looking up

. (So the baptism for Mary and her Dad's dc will be good starters)
Cheers, JM