You have said
Children from marriage Jacob 1833,Thomas 1849,Levi 1851-1931, Susan 1853-1924.
I assume this is from her 1847 marriage to William PURDY and if so please could you give the correct date for Jacob
And these children registered in NSW, parents William, Elizabeth
1856 William E PURDY, reg O'Connell Town, #2184 - died 1857 (reg Glebe, #1627)
1858 William, reg Glebe, #2568 - died 1917 (reg Kogarah, #4219)
1859 Sarah A, reg Goulburn #7572 - died 1861 (reg Goulburn, #2912)
1862 Mary J PURDAY, reg Goulburn #7616
Have you definitely ruled out the Elizabeth SMITH died in Hay 1879? I know the mother's name is incorrect in the index record.
NSW 1879 Elizabeth SMITH, reg Hay #5975
Parents: Isaac D, Alexandrina
Judith