Hi there,
I am not a descendant of Elizabeth SMITH.
So if I am understanding this, you are currently thinking that Elizabeth SMITH (born 1799 as her info based on her headstone) was the daughter of Mary HEARNE (born 1790) who married Henry COOPER.
May I ask about how and when Mary HEARNE arrived in New South Wales. (add, as either Hearne or Buckland, as Elizabeth was noted on a NSW 1820s General Muster as born in the colony).
I can see that Joseph SMITH arrived Sydney NSW per the Neptune 1790, and had been tried at the Old Bailey in Sept 1789. I cannot find Mary HEARNE or Henry COOPER arriving to NSW before 1800. I can find Mary FLANIGAN who arrived 1815 per Francis & Eliza, she was born about 1790 in Dublin, Ireland. in the 1828 NSW census she was recorded as mary HEARN, free by servitude, with John HEARN, Lower Portland Head (the then local name for what is now referred to as Macdonald River).
JM