Bibles were also commonly given to parents for a child at the time of birth. So this, just possibly, could indicate the birth of Mary Croker.
Now, this is a longshot, but some Ancestry family trees have a Mary Croker who goes to Australia from Ireland and marries a John O'Keefe. It might be worth looking this person up, if only to discount her from your enquiries.
Only problem is that they have her born in 1817, not 1816. However, birth years are often mis-recorded. Unfortunately my level of access limits what I can see for non-British records, so I don't know what they are using to back up their research.