Trove was not entirely in agreement...but mostly..
1862 'SHIPPING.', The Age (Melbourne, Vic. : 1854 - 1954), 17 March, p. 4. , viewed 21 Jan 2021, http://nla.gov.au/nla.news-article154847400
Shackamaxon, Black Ball ship, 987 tons. J. B. Fulton,
from Liverpool, 23rd December, with 345 Government im
migrants; W. G. Gunn, M. D. Surgeon Superintendent.
Bright Brothers and Co , agents.
Shackamaxon, Black Ball ship, 989 tons, J. B. Teulou,
from Liverpool December 23rd, with 345 Govern-
ment immigrants. W. G. Gun, Esq., M.D., surgeon
superintendent. Bright Brothers and Co., agents.
1862 'PUBLIC TELEGRAM.', South Australian Register (Adelaide, SA : 1839 - 1900), 19 March, p. 2. , viewed 21 Jan 2021, http://nla.gov.au/nla.news-article40470128
Melbourne Shipping.— Arrived— March
16. Shackamaxon ship from Liverpool.
1862 'SHIPPING INTELLIGENCE.', The Argus (Melbourne, Vic. : 1848 - 1957), 20 March, p. 4. , viewed 21 Jan 2021, http://nla.gov.au/nla.news-article5711940
The Ship Shackamaxon, with her Government immigrants on board, was towed alongside the Government Railway Pier, Williamstown, yesterday morning. Her passengers were forwarded to Melbourne by special train.
Doesn't seem to be an easy one to find details for.