It is thought that Eliza was the first European woman to have official duties in Australia as "First Lady" to her husband's uncle who was the second Governor of New South Wales.
She spent five years travelling on board a ship and wrote about her visit to New Caledonia and one of her voyages from New South Wales to England.
At the beginning of 1795 the family set off on HMS Supply under her husband's command bound for Sydney en route to New South Wales.
On 16 February, they sailed for New South Wales accompanied by Captain John Hunter in HMS Reliance.
[1] The ships arrived at Sydney on 7 September, and for the next five years Kent was employed in the service of the colony, making voyages to Norfolk Island and the Cape of Good Hope, and surveying parts of the coast of New South Wales.