The first British colony in Australia, New South Wales, was founded in 1788. Six colonies (including the island of Tasmania) joined together to form the Commonwealth of Australia in 1901.
TROVE - National Library of Australia's digital archive. Includes millions of items: historic newspapers, magazines, images, maps, books, etc.
"Aborigines" - books, serials, etc. relating to indigenous Australians, 1830s-1910s
Exploration Reports - published accounts of British/Australian expeditions to the interior of Australia, 1829-1900s
Missionary Reports - mostly relating to conversion of Australian indigenous peoples, 1837-1915
New Zealand was adminstered as part of Britain's New South Wales (Australia) colony from 1788-1835. It was a separate colony beginning in 1841, and became a self-governed dominion in 1907.
DigitalNZ - Over 30 million digitized archives, books, images, audio-visual files, etc. about New Zealand. Tip for Browsing: Scroll to the bottom of the page and choose a decade; when you get the results, choose the "More" tab, and then select Books, Archives, Manuscripts, etc.
Government Patrol Reports (under Australia), 1900s+ : Several dozen patrol reports created between 1900-1920, apparently showing how the government kept Natives corralled in villages as forced laborers.
Western Pacific Territories
Britain's Western Pacific Territories included Fiji (1877-1970); Tonga (1900-1952); British Solomon Islands (1893-1971); and more.