That anecdote doesn't pass the smell test. The article says "the 1860's". Quoth wikipedia: «The last convict ship to be sent from England, the St. Vincent, arrived in 1853». Another source[1] states that the worst death rate of the fleet was 33%, far below the 60% in your source.

Makes for a great story/example though! Which I guess is how these anecdotes propagate.

[1] http://www.historyaustralia.org.au/ifhaa/ships/2ndfleet.htm