Hello,
I now have a copy of Jane's death certificate. It gives a tiny bit more information. Jane's birth is probably closer to 1819 than 1817 and her father Robert was an Innkeeper.
Jane SANDS
Date of Death: 20 Sep 1890 Braidwood, NSW
Occupation: - Age: 70
Place of Birth: Scotland - 40 years in Colonies
Father: Robert ANDERSON - Innkeeper
Mother: Maggie (Surname not stated)
Place of Marriage: Scotland
Age at Marriage: 25
Name of Spouse: James SANDS
Children: No Issue
Informant: James SANDS, Husband, Braidwood
Cause of Death: Senile Decay - 6 weeks
Medical Attendant: Dr FLORANCE 20 Sep 1890
Date of Burial: 22 Sep 1890 Braidwood
Minister: Rev J S DOBSON (Religion not stated)
Undertaker: R McDONALD
Witnesses: C O'LOUGHLIN, Alexr McRAE
Registered: 22 Sep 1890 Braidwood
Ref#: 1890/3378
I'm not so sure about the 'Maggie' being correct but I'd say father 'Robert ANDERSON an Innkeeper' is probably more likely to be correct.
I still think Jane/Janet/Jean if not born in Culross, Perthshire or West Lothian or Fife then was probably in one of those places in 1841 census.
Jane married in 1844 in Dunfermline, Fife and in 1841 her future spouse was living in Dunfermline.
Would some kind person please look again and see if Jane/Jean/Janet ANDERSON born abt 1819 and father Robert an Innkeeper can be found in 1841. Most likely place Dunfermline, Fife because her future spouse was a weaver and had no reason to be travelling out of the city for them to have met between 1841 and 1844. I am guessing now.

Damn it if he was a 'Journeyman weaver'
Addition: Of course, Jane may not be with her parents in 1841.
Thanks.
Dave