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Queensland became a separate self-governing colony in 1859. First European settlement was temporarily established at Redcliffe in 1824, later moved to present day Brisbane, as Moreton Bay penal settlement. The penal colony closed in 1839. From 1842, free settlement commenced, especially to the north of Brisbane, with the Port of Maryborough opening in 1847.
The Queensland Government’s Immigration site holds an array of records: Immigration | Queensland Government
Immigrants landed at various locations along the coast, with entry ports being Moreton Bay (BrIsbane), Maryborough, Bowen, Bundaberg, Cairns, Gladstone Mackay, Rockhampton, Thursday Island and Townsville.
If you know which port your forbears arrived at, it's worthwhile seeing what records the local historical society may hold, in addition to State records.
Overland travel from NSW began as early as 1827, when botanist/explorer Allan Cunningham travelled inland from Newcastle, then up the Hunter Valley, to cross the Great Dividing Range and head northwards to discover the Darling Downs pastoral region.
Geoff Ginn provides a good summary of the early days of the Queensland pastoral industry - Pastoralism 1860s-1915 | Queensland Historical Atlas
Note: The Queensland Historical Atlas provides numerous engaging articles and resources, describing aspects of Queensland history (early and modern) and culture.
Assisted Immigrants
The indexes below provide Last Name, First name, Age, Ship, Arrival Date and Qld Archives Page number, but NOT which port.
Actual records are held at Qld State Archives
Assisted immigration 1848 to 1912 - Dataset - Open Data Portal | Queensland Government
The State Library of Queensland holds many collections to help your family history research - Family history | State Library of Queensland
Spend some time browsing as you may uncover ideas for new lines of enquiry.
History of Brisbane - History of Brisbane - Wikimedia Commons
Maps - Old_maps_of_Brisbane
20th century photos of Qld, which may be helpful for illustrative purposes/setting visual context: Photographs of Queensland - Wikimedia Commons
South Sea Islanders - Between the 1863 and 1904 an estimated 40,000 to 60,000 South Sea Islanders entered Queensland, predominantly as labourers to work on sugar plantations: Australian South Sea Islanders