The point is that the NZ info will help you find the NBL info.
If you have all the NZ info, what does Ann Charleton's NZ 1876 death cert give as the names of her parents and her birth place? According to the info on the DIA website, this started to be included from 1876.
If you have all info from their arrival in NZ, what is the family info that John Charleton, son of George and Ann, would have had to supply in support of his claim to the estate of Robert Robson, who John believed was the brother of his mother Ann Robson/Charleton?
You actually have some rich sources available to you in NZ and it does not appear from your questions that you have yet followed these up. There is little point guessing which (if any) baptism might be yours when you have easily accessible ways of being more certain.