There are several very comprehensive collections of records concerning the people exported to Australia from the United Kingdom between 1788 and 1866.
The Convict Database has been compiled from British Home Office (HO) records which are available on microfilm as part of the Australian Joint Copying Project (AJCP). The HO 11 Criminal – Convict Transportation Registers series has been indexed by the State Library of Queensland and the index contains the following information:
Name of convict, including any known aliases
Place of trial *
Term of years
Name of ship and date of departure
Place of arrival
Miscellaneous notes e.g. Died at sea; Ticket of Leave, etc.
* The date of trial is recorded on the original registers and will be gradually added to this database
A search of that database indicates that there were 53 convicts named Leach among the 123,000 records and that 1812 was a particularly bad year for men of that name. There were three among the 200 convicts aboard the Fortune when it sailed in November of that year (reaching Sydney in 1813)
Title: Thomas Leach, one of 200 convicts transported on the Fortune, November 1812.
Details: Sentence details: Convicted at Middlesex Gaol Delivery for a term of 14 years on 10 July 1811.
Vessel: Fortune.
Date of Departure: November 1812.
Place of Arrival: New South Wales.
Source: Australian Joint Copying Project. Microfilm Roll 87, Class and Piece Number HO11/2, Page Number 85 (44)
Record number: 1103363
Link to this record: http://onesearch.slq.qld.gov.au/primo_library/libweb/action/dlDisplay.do?vid=SLQ&docId=slq_voyager1103363
Title: Robert Leach, one of 200 convicts transported on the Fortune, November 1812.
Details: Sentence details: Convicted at Middlesex Gaol Delivery for a term of life on 15 January 1812.
Vessel: Fortune.
Date of Departure: November 1812.
Place of Arrival: New South Wales.
Source: Australian Joint Copying Project. Microfilm Roll 87, Class and Piece Number HO11/2, Page Number 86
Record number: 1101510
Link to this record: http://onesearch.slq.qld.gov.au/primo_library/libweb/action/dlDisplay.do?vid=SLQ&docId=slq_voyager1101510
Title: James Leach, one of 200 convicts transported on the Fortune, November 1812.
Details: Sentence details: Convicted at York County Assizes for a term of life on 07 March 1812.
Vessel: Fortune.
Date of Departure: November 1812.
Place of Arrival: New South Wales.
Source: Australian Joint Copying Project. Microfilm Roll 87, Class and Piece Number HO11/2, Page Number 90
Record number: 1101892
Link to this record: http://onesearch.slq.qld.gov.au/primo_library/libweb/action/dlDisplay.do?vid=SLQ&docId=slq_voyager1101892
Of course, all of that is based on the assumption that the putative convict father's name was Leach. If it was not, then you can use these links to run your own searches.
Update
And if it happens that Esther is actually Esther Locke (who married William Watson in 1842) then her father might well be
Title: Stephen Locke, one of 200 convicts transported on the Fortune, November 1812.
Details: Sentence details: Convicted at Surrey Assizes for a term of life on 27 July 1812.
Vessel: Fortune.
Date of Departure: November 1812.
Place of Arrival: New South Wales.
Source: Australian Joint Copying Project. Microfilm Roll 87, Class and Piece Number HO11/2, Page Number 89 (46)
Author/Creator: Great Britain. Home Office. ; State Library of Queensland.
Subjects: Locke, Stephen ; Fortune (Ship) ; Convicts -- Australia -- Registers ; Australia -- Genealogy
Publisher: Canberra A.C.T. : Australian Joint Copying Project
Is Part Of: Criminal : Convict transportation registers [HO 11]
Record number: 1101887
Link to this record: http://onesearch.slq.qld.gov.au/primo_library/libweb/action/dlDisplay.do?vid=SLQ&docId=slq_voyager1101887
