Fishburn appeared in the 1781 volume of Lloyd's Register with Gill, master, J.Pierton, owner, and trade Cork-based transport.

Her master for the voyage to Botany Bay was Robert Brown, and she was owned by Leighton Co., who were also the owners of Golden Grove and Borrowdale.

The shortfall was made up through forced transfers from HMS Hyaena, the Royal Navy escort ship that accompanied the Fleet for the first three hundred miles of its voyage.

She left Port Jackson on 19 November 1788, keeping company with Golden Grove until losing sight of her on 11 April 1789 after several days at the Falkland Islands for recovery of crew members who were sick with scurvy.

The fate of Fishburn is unknown; she appears to have disappeared from the records after being discharged from Her Majesty's service at Deptford, nine days after her arrival.