Passenger list on arrival at Port Jackson (Sydney harbour) shows:
John Stone, 40, Farm labourer, born London Middlesex, religion Church of England, can read and write.
Rebecca 36, wife, born London Middlesex, CoE, read and write
Rebecca Mary 5, daughter, born Norwood Surrey, CoE, read
John Thomas 3, son, born Norwood Surrey, CoE
Henry (Infant), son, born Norwood Surrey, CoE
Mariners and ships in Australian Waters
"KATE"
SHIP, TONNAGE 904, MASTER BRODRICK, SAILED 14TH JUNE 1849 FROM WHENCE, LONDON TO PORT JACKSON (Sydney Harbour), 23RD SEPT 1849
Seems John Stone and a dozen other passengers were summond (by letter) by the Immigration Board on 26 Oct 1849 to 'attend a Board meeting to discuss the Surgeon Superintendent' - John had previously declared he had no issues with his treatment on board! [https://www.records.nsw.gov.au/archives/collections-and-research/guides-and-indexes/node/14210046/browse].