In 1804 she took part in a series of voyages to Van Diemen's Land with the aim of founding a colony at Port Dalrymple, the site of the modern settlement of George Town, Tasmania.

[2] King was impressed with the work despite this variation from the original plans; in a letter to Lord Hobart, Secretary of State for War and the Colonies, he praised the speed and quality of Integrity's construction and described her as "extremely well put together and strong".

[5] The newly built vessel was launched on 13 January 1804 as "His Majesty's Armed Colonial Cutter Integrity" under the command of Royal Navy Lieutenant John Houstoun and with a crew of eight men.

[8] Integrity's first voyage was in February 1804, heading south along the eastern coastline of Australia to transport settlers and supplies across Bass Strait to the colonial outpost in Van Diemen's Land.

Governor King now directed that Bowen travel back to Van Diemen's Land aboard Integrity in order to formalise the transfer of colonial authority to his successor.

With Lieutenant Houstoun again in command, the cutter was to transport Lieutenant-Colonel William Paterson to the north of Van Diemen's Land in order to found a new settlement at Port Dalrymple.

To support the settlement, the cutter was also assigned to carry nineteen soldiers of the New South Wales Corps, a ship's surgeon and ten convicts.

The cutter would then proceed to Cape Barren Island, a remote location in Bass Strait, to investigate rumours that a group of American sailors were establishing an unlawful trade in seal skins.

[19][20] In September she sailed a round trip to the New South Wales colony of Newcastle to ship a cargo of cedar wood back to Port Jackson, followed by another brief voyage to Norfolk Island.

[20] Lieutenant-Colonel Paterson and the principal colonists would travel aboard Buffalo but transfer to Integrity if the Navy vessel was too large to enter the bay where the settlement was proposed to stand.

Captain William Kent of Buffalo signaled for the flotilla to take in their sails and ride out the storm; on the following morning the crew of Integrity discovered that they had lost sight of all three other vessels and were running dangerously close to a lee shore.

[30] For the voyage she was again under the command of Acting Lieutenant Robbins, with a crew of ten men and bearing a flag of truce "in case war should have taken place between England and Spain" before she reached her destination.

Historian Frank Bladen has conjectured that the cutter either foundered en route, or reached South America but was captured by an indigenous tribe.

[32] A year after Integrity's departure, on 20 July 1806, King wrote to Viscount Castlereagh expressing concern at the cutter's continued absence and hoping that she had simply been detained by Spanish authorities.

[33] She was last mentioned in a report on colonial shipping compiled by Governor King in August 1806 – fourteen months after her disappearance – with details of pay still owing to her crew and accompanied by the annotation "Gone to Valparaiso ... Not returned.