Jacarandas were brought from South America. Reputedly the first Jacaranda tree grown in Australia is/was in the Brisbane City Botanic Gardens.
Brisbane claims the earliest jacaranda tree in Australia, planted in 1864, but the Sydney Botanic Garden jacaranda is dated at “around” 1850, and jacarandas were listed for sale in Sydney in 1861.
Either way they've been here quite a while, and longer than many family lines that consider themselves Australian. The midwife story I mentioned is also contentious because there are a few myths going around about North Sydney in particular, but I think the one from Sutherland had some facts backing it up, including a man who remembered gathering them as a child.