Hi guys (and Rhonda), I am also researching the Basham heritage, especially as it applies to the family in and around Victor Harbor/Port Elliot in South Australia and the subsequent link to the Gray family.
Info that may help:
On 27 March 1817 the vessel Cochin left Port Jackson, Sydney, and arrived at the Derwent in Tasmania on April 6/7 1817. Sources: Nicholson, Ian Hawkins, Shipping Arrivals and Departures, Tasmania, 1803-1833, Roebuck, 1983, p45.
Newspaper report The Hobart Town Gazette and Southern Reporter, Saturday 12 Apr 1817, p2.
The passengers on that vessel included Sarah Basham (nee Ashby) and her four children. Additional source: Tasmanian Immigrants List "B" surnames Basham Sarah (nee Ashby) and four children ship Cochin (1817) contact Erin O'Donnell.
Sarah Basham is also mentioned in the Trove digital newspaper The Southern Argus (Port Elliot,SA: 1866-1954) under DIED: On the 23rd September at her residence, Launceston, Tasmania, Mrs Sarah Basham, mother of Mr William Basham, of Port Elliot Mill, and grandmother to William and Charles Basham, of Port Elliot, and Jonathan Basham, of Hindmarsh Valley, aged 99 years (this refers to Sarah). A colonist of 51 years.
This Trove entry confirms Sarah's arrival in Tasmania (1817) and gives a birth year of 1769 for her. She would have been 48 on her arrival in Tasmania. And she is not listed as a convict. Someone else has mentioned that she originally went to Sydney to join her "miscreant" husband, who had been shipped off to the colonies after being found guilty of a crime in England (just cannot put my finger on this posting at the moment).
One of Sarah's grandsons, Jonathan Samuel Basham, was born in Launceston, Tasmania, on May 12, 1828. He sailed to Port Adelaide in South Australia aboard the vessel Fox, arriving in 1939. He took up farming in the Hindmarsh Valley area near Victor Harbor. There are two conflicting reports of his marriage to a Susan Paget by whom he produced 11 children, including Frederick Basham (1863-1939) who married Sarah Jane Gray (1864-1923). He died on April 1, 1902.
Hope this helps and I am always happy to receive "corrections". I have an Ancestry tree that I am happy to share.
Best regards
Dennis