And you should never own to a mosquito. I once unfortunately stated to a Queensland gentleman that my coat had been bitten by cockroaches at his brother’s house, which I had just left. ‘You must have brought them with you then,’ was the fraternal defence immediately set up. I was compelled at once to antedate the cockroaches to my previous resting-place, owned by a friend, not by a brother. ‘It is possible,’ said the squatter, ‘but I think you must have had them with you longer than that.’ I acquiesced in silence, and said no more about my coat till I could get it mended elsewhere.— Anthony Trollope, Australia and New Zealand, London: 1873, 67.
To repel the Cock-roach. — Take a small quantity of white arsenic finely pulverised, strew it on crumbs of bread, and lay it near their haunts; a few nights will suffice.
And even earlier, in 1820, Lt. (later Admiral) King tried to deal with pests in the cutter he was using to map Australia's coasts:— Launceston Advertiser, 20 December 1830, 4, http://trove.nla.gov.au/ndp/del/article/84776042
The cutter was careened at a place appointed for the purpose on the east side of Sydney Cove; and whilst undergoing her repair the crew lived on board a hulk hired for the occasion. This offered so favourable an opportunity for destroying the rats and cockroaches with which she was completely overrun, a measure that, from the experience of our last voyage, was considered absolutely necessary for our comfort as well as for our personal safety, that, as soon as the operation of coppering and caulking was finished, she was secured alongside of the hulk, and there immersed in the water for several days, by which process we hoped effectually to destroy them.Upon the vessel being raised and the water pumped out, I was rejoiced to find that the measure appeared to have had the desired effect; but, before we left Port Jackson, she was again infested by rats, and we had not been long at sea before the cockroaches also made their appearance in great numbers. In sinking the cutter it seemed, in respect to the insects, that we had only succeeded in destroying the living stock, and that the eggs, which were plentifully deposited in the recesses and cracks of the timbers and sides, proved so impervious to the sea-water, that no sooner had we reached the warmer climate, than they were hatched, and the vessel was quickly repossessed by them; but it was many months before we were so annoyed by their numbers as had been the case during the last voyage.— Lt. P. P. King, Narrative of a Survey of the intertropical and western coasts of Australia.