Thank you so much. I had most of that information but the 1941 Census of Fanny aged 15 is of most interest. I think there is a mistake with her birth being 1836 - as in 1841 she would be 5 years old. G grandmother Fanny was christened in 1829 the same year as James and Sarah married. So I think it is conceivable that this Fanny you have found is our girl. She would have been 13/14 in 1841 if she was born in 1828/29. Also I found Charlotte her sister was on the census being 10 years old and working. This leads me to believe that when Fanny lists she arrived in Australia on the "Royal Admiral" that information is correct - the last voyage of that ship was in 1842 and it was an all female convict transportation except for two free women and nine children. I think Fanny and her sister Charlotte may have been among those children. I am trying to find out where the original ship's manifest is held. In 1844 that ship sank off the coast of India.
Apparently Earl Grey had set up a reunification for wives and families of convicts and they were transported to the colony by the Australian and British Governments. Unfortunately on the passenger lists they didn't identify children. Also I wonder what happened to Sarah White nee Forester?
Again thanks you so much for your help that has given me renewed hope in piecing this puzzle together.