The child and mother are both named, as well as the name of her ship?
Debra 
Yes, David Wall, Marg
t Wall, Mermaid
I think now that the death record holds the clue as it says "Prisoners child" rather than "Convicts child".
Margaret Wall (alias Burton) was in and out of prison including in the Female Factory near the middle of 1830 around when David Wall (died at 2 years 6 months) would have been born.
David William Wall was baptised 21 December 1830, so closer to 2 years old in Jan 1833.
Mary was assigned soon after arrival, and only entered the Female Factory in 1834, so you would expect it to read "Convicts child"
So, unless something else turns up, the David Wall who died in 1833 was not the same child who arrived with Mary Wall
M
