Looks like I need to answer it myself. On the shipping list amongst the "single women" is Ann Wheatley aged 17 from Sussex. It was the custom to list females over the age of 15 as "single women" in the passenger list. As she was 5 years older than her nearest sibling they would all have simply been listed as "family". John Wheatley was a firebrand preacher and being a Wesleyan Methodist he and his family were no doubt classified as religious dissenters and that is the religion listed for the Ann on the William Metcalfe. As such it is hardly likely that he would let his daughter travel alone on the ship.
At the following link is a copy of the Sydney Morning Herald, Wednesday 5 September 1838, which has a passenger list for the William Metcalfe which includes John Wheatley, wife and seven children. Listed as a shoemaker and farmer.
His eldest daughter was an Ann and on arrival she would have just had her 17th birthday. They came from Sussex. That will do me.