Froude, James Anthony (2010) [1886]. Oceana, Or, England and Her Colonies [the colonies of modern day Australia). Cambridge University Press. pp. 19, 92. ISBN9781108023900. — page 19 for details of the specific ship SS Australasian (1884). The full sentence on page 92 is "She had safely carried us down under as the Square gardener put it to me afterwards in London, scarcely believing it could be a reality".
oed.com
Oxford English Dictionary (Electronic), Version 4.0, entry for "down under". The dictionary recodes the first published use in 1886 by J. A. Froude in "Oceana" p. 92 "We were to bid adieu to the 'Australasian'…She had carried us safely down under."