The Rolla was built at Shields in 1800. She was the next convict ship to leave Ireland bound for New South Wales after the departure of the Atlas in May 1802.
The London Times reported that the Rolla sailed from Portsmouth, however after receiving some damage in a gale of wind was blown into the Downs. She was at Deal on 15th February 1802 preparing to put into the river to make repairs. 
Prisoners of the Rolla came from counties throughout Ireland including Cavan, Dublin, Meath, Cork, Clare, Kilkenny, Limerick, Armagh and Kildare.
Find out more about the convicts from Armagh - Patrick Hand, Hugh Kelly, Cormac McCain, William McDaley and John Murray in Armagh Convicts in Australia, 1800-1806 by Anne-Maree Whitaker.
The Rolla departed Cork on 4 November 1802.
Rio de Janeiro
They arrived at Rio de Janeiro on 12th January after a passage of 72 days. The convicts were very quiet and there was no loss of life until after arrival at Rio when a male convict died suddenly.
They sailed from Rio on 6 February 1803. During the voyage there was much bad weather in the course of which the Rolla sprung the main mast and carried away her main yard. 
After a voyage of 95 days they came to anchor at Port Jackson on 12 May 1803. A few of the convicts were suffering from slight scurvy however the rest were of general good health. . Seven or eight convicts died on the passage out.
The Rolla brought Government supplies - 234 tierces of pork, 686 casks of flour and 11 tons of sugar.
Around 1803 convict artist John William Lancashire produced the watercolor 'View of Sydney taken from The Rocks'. The stone bridge of the Tank Stream is on the extreme right while Government House is centrally located. This is the layout of Sydney Town as the convicts of the Rolla would have known it.
Departure from Port Jackson
The Rolla left Port Jackson on 20 September 1803 in company with the Cumberland with Matthew Flinders on board and the Francis on their way to the shipwrecked vessel Porpoise .....Tales of Shipwrecks. On board the Rolla was a stowaway convict James Alder. (See HRA, Vol IV, p. 423)
They called at Port Stephens on the way sheltering from bad weather there overnight. The Rolla's top gallant sail was the first seen by the survivors of the Porpoise who were overjoyed at Flinders' return.......
On the 7th of October, a little before noon, a sail was descried in the eastern quarter; in a little time another, and soon after a third was discovered. Their emotions at the sight of these can better be conceived than described. Indeed the astonishment on board these vessels was equal to their own; for, on that very day the Resource (their own production) had gone to Turtle Island, by way of trying her, and they little expected to be met by a schooner of 20 tons, erected in this island, considering the short space of time, and the implements they had to work with.
As these vessels approached they perceived the largest to be the Rolla, convict ship, which they had left in Sydney Cove, the others were the Frances and Cumberland, colonial schooners, which were familiar to them. In the afternoon all three vessels anchored to leeward of the reef, and a boat put off soon after from the Cumberland, in which, as she neared them, they saw Captain. Flinders who received a hearty cheer on landing. For the last ten days preceding the arrival of these vessels they had every night at eight o'clock, fired a great gun by way of apprising them of their situation, if chance should have brought them at dusk near to the reef.
Notwithstanding six weeks had expired from the time Captain Flinders had left them, they did not think it proper to adhere to the agreement that was made between them, and therefore had no intention of quitting the island yet. They naturally concluded that he might have had a tardy passage to Port Jackson, and even when he got there, that vessels might not have been in readiness in Sydney Cove to send to their assistance. He might also, from the fatigue of going there, have been incapacitated from returning immediately, and thus the sailing of a vessel might have been procrastinated. These and other considerations made them change their former resolutions; and it was agreed never to separate, but wait patiently till another boat should be built, and go in a body together. Had they parted, as it had been previously planned, at the end of six weeks, it would in all probability have been productive of much uneasiness and dissatisfaction, as well to those who went from, as to those who remained on the reef... (from)The mariner's chronicle; or Interesting narratives of shipwrecks.
The Francis returned to Sydney and Matthew Flinders continued on his ill-fated voyage on the Cumberland. Lieutenants Fowler, Flinders (Matthew Flinders' brother), and John Franklin sailed with the Rolla to China.
The Times reported on 12th October 1804.... His Majesty's ship Courageux came from St. Helena with the following East Indiamen under convoy - City of London, Ceylon, Calcutta and Wyndham, the Rolla, Cumming from Botany Bay and the Lively and Vulture from the South Seas. It appears that the fleet has experienced the most tempestuous weather during their passage. In the latitude of the Cape a most tremendous gale came on; the Prince of Wales was seen in the utmost distress, and from the floating pieces of wreck that the fleet fell in with two days after, it is feared that she went down, and every soul on board perished.
Notes and Links
1). National Archives - Voyages: (1) 1802/3 New South Wales and China. Capt Robert Cumming. Cork 4 Nov 1802 - 22 Sep 1803 Port Jackson - 14 Dec Whampoa - 31 Jan 1804 Second Bar - 14 Mar Malacca - 13 Jul St Helena - 9 Oct Downs.
2). Andrew Doyle was one of the convicts of the Rolla. His wife Sophie and their three children including son Cyrus Matthew Doyle arrived as a free passengers on the Rolla.
3). Edward Hyland was indicted for having stolen two silver cups, the property of Henry Westray Esq., - The first witness was Ann Doyle, examined by Mr. Bethel; she deposed that she was in the service of Mr. Westray, and that on the 19th of September last, she perceived the prisoner at the bar running out of the hall door; that she followed, had him apprehended, and the cups, which were her master's property, taken from him. The recorder asked the prisoner if he had any thing to say in his defence, and he answering in the negative, was found guilty ,and received sentence to be transported for seven years. - Freeman's Journal 16 October 1800
4). Convicts of the Rolla later located in the Hunter Valley region:
Mary Higgins/ Tyrrell
Margaret Doyle/ Lawrence
(1) 'Ship News.' Times [London, England] 17 Feb. 1802: 3. The Times Digital Archive. Web. 10 Mar. 2013.