Major Thomas Mitchell, Surveyor-General of the Colony of New South Wales from 1828 to 1855, undertook several journeys of exploration. His third, in 1836, took him south into what is now Victoria. On 10 July he recorded in his journal that he and his party
crossed a deep creek running westward which I named the Avoca, and we encamped on an excellent piece of land beyond it.
Mitchell, Thomas, Sir, 1792-1855 (1839-01-01). Three expeditions into the interior of Eastern Australia : with descriptions of the recently explored region of Australia Felix and of the present colony of New South Wales. T. & W. Boone volume 2 retrieved through http://gutenberg.net.au/ebooks/e00036.html
Mitchell was born and raised in Scotland not Ireland. The inspiration for the name probably came from Thomas Moore’s 1807 poem ‘The Meeting of the Waters’. The final stanza has:
Sweet Vale of Avoca! how calm could I rest
In thy bosom of shade, with the friends I love best;
Where the storms that we feel in this cold world should cease,
And our hearts, like thy waters, be mingled in peace.

Currier & Ives & Moore, T. (1868) The meeting of the waters. In the Vale of Avoca, County Wicklow Ireland
. County Avoca Ireland Wicklow, 1868. [New York: Published by Currier & Ives 152 Nassau St. New York] Retrieved from the Library of Congress, https://www.loc.gov/item/2002710554/.
In the 1850s the town of Avoca was established on the Avoca River. Greg’s great great grandfathers George Young and John Plowright were gold miners there.
My Cudmore relatives had a property on the Darling River named Avoca. We visited it earlier this year. It was said that Daniel H. Cudmore named it Avoca after his father’s hometown in Ireland. However his father, Daniel M.P. Cudmore, was from Limerick Ireland. I am not aware of any connection of the Cudmore family to the town of Avoca in Ireland.

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