Queen departed from Cork, Ireland; naval agent, Lieutenant Samuel Blow.
Correspondence written on 24th April 1791 at Madeira possibly by Lieut. Young who had charge of the Albemarle notes the day the Albemarle parted from the other ships...We are now very peaceable, and I am in hopes shall continue so during the remainder of the voyage. The Matilda parted company the first night we left Portsmouth, the Active and Britannia on the night of the 3rd (April), and the Admiral Barrington on the 7th in hard gale of wind. 
Lieut-Gov. King at Port Praya, St. Jago writing to Under Secretary Nepean on 3rd May 1791....The Admiral Barrington anchored here this afternoon. This ship and the Britannia were in Mr. Young's division, and parted company with him near Cape Finisterre.....The convicts as well as the soldiers have been troublesome on board the Britannia, by the master's account. The Barrington has buried five convicts and the Britannia three. They are both very healthy. 
The New South Wales Corps formed the Guard on the vessels of the Third Fleet.
Arrival at Port Jackson
The Britannia arrived at Port Jackson on 14 October 1791, the day after the Albemarle. Twenty-one prisoners had died on the passage out.
Some of the vessels of the Third Fleet were to proceed to the Southern Whale Fisheries after unloading the prisoners; the rest were bound for Bengal where they were to be freighted back to England with cotton. The sailors on board the Nootka ships were to have nine guineas for the run to Botany Bay after which they were to share as whale fishermen do. The other sailors were paid twenty-five shillings per month. 
The Britannia left for the Southern Whale fishery on 28th October 1791.
Extract of Thomas Melville's Letter to his owners in London, on the subject of establishing a Sperm- Whale Fishery in New South Wales.
'Ship Britannia, Sydney, Port Jackson,
Nov. 29th, 1791.
'Gentlemen, 'I have the pleasure to inform you of our safe arrival in Port Jackson, in New South Wales, after a passage of fifty-five days from the Cape of Good Hope.
'The day before we made the island of Amsterdam, we saw two shoals of sperm whales. After we doubled the south-west cape of Van Diemen's Land, we saw a large sperm whale off Maria's Islands, but did not see any more, being very thick weather and blowing hard, till within fifteen leagues of the latitude of Port Jackson. Within three leagues of the shore we saw sperm whales in great plenty: we sailed through different shoals of them from twelve o'clock in the day till after sunset, all round the horizon, as far as I could see from the mast-head: in fact, I saw a very great prospect in making our fishery upon this coast, and establishing a fishery here.
Our people were in the highest spirits at so great a sight, and I was determined, as soon as I got in and got clear of my live lumber, to make all possible dispatch on the fishery on this coast.
'On our arrival here, I waited upon His Excellency Governor Phillip, and delivered my letters to him. I had the mortification to find he wanted to dispatch me with my convicts to Norfolk Island, and likewise wanted to purchase our vessel to stay in the country; which I refused to do. I immediately told him the secret of seeing the whales, thinking that would get me off going to Norfolk Island, that there was a prospect of establishing a fishery here, and might be of service to the colony, and left him. I waited upon him two hours afterwards with a box directed to him: he took me into a private room; he told me he had read my letters, and that he would render me every service that lay in his power; that next morning he would dispatch every long-boat in the fleet to take our convicts out, and take our stores out immediately ; which he did accordingly, and did everything to dispatch us on the fishery.
Captain King used all his interest in the business. The secret of seeing whales our sailors could not keep from the rest of the whalers here: the news put them all to the stir, but have the pleasure to say, we were the first ship ready for sea, notwithstanding they had been some of them a month arrived before us. We went out, in company with the William and Ann, the eleventh day after our arrival. The next day after we went out, we had very bad weather, and fell in with a very great number of sperm whales. At sun-rising in the morning, we could see them all round the horizon. We run through them in different bodies till two o'clock in the afternoon, when the weather abated a little, but a very high sea running.
I lowered away two boats, and Bunker followed the example: in less than two hours we had seven whales killed, but unfortunately a heavy gale came on from the south-west, and took the ship a-back with a squall, that the ship could only fetch two of them; the rest we were obliged to cut from, and make the best of our way on board to save the boats and crew. The William and Ann saved one; and we took the other, and rode by them all night with a heavy gale of wind. Next morning it moderated, and we took her in; she made us twelve barrels. We saw large whales next day, but were not able to lower away our boats: we saw whales every day for a week after, but, the weather being so bad, we could not attempt to lower a boat down. We cruised fifteen days in all.
The day after we came in, the Mary Ann came in off a cruise, having met with very bad weather, shipped a sea, and washed her try-works overboard. He informed me he left the Matilda in a harbour to the northward, and that the Salamander had killed a forty-barrel whale, and lost her by bad weather. There is nothing against making a voyage on this coast but the weather, which I think will be better next month: I think to make another month's trial of it. If a voyage can be got upon this coast, it will make it shorter than going to Peru. 'The colony is all alive, expecting there will be a rendezvous for the fishermen. We have the pleasure to say, we killed the first four whales on this coast. I am, Sirs, your humble servant, Thomas Melville, Messrs. Samuel Enderby and Sons.' 
Notes and Links
1). Convict John Bird died in 1793. He was buried in the Old Sydney burial ground
2). Captain Bunker on the William and Ann and Thomas Melville on the Britannia were two of the first men who embarked on whaling voyages in 1791.
 Historical Records of Australia, Vol.1, pp. 225, 488, 489
 Lang, John Dunmore, An historical and statistical account of New South Wales: Volume 1, p.459