Most people in Australia know of the extremes of the place. So major fires, droughts, floods, storms and cyclones are only a matter of when, rather than if.
It's not a 1000 year flood. These types of things happen at least once every 50 years (plus more frequent minor floods) going back about 170 years to the written history. The major dam built to mitigate (not prevent) flooding arguably might have performed better to lower the peak, but the flood event came after a month of record rainfall, and the dam operators followed the manual given to them. That might need review for future operations, but it's not like someone did something rash or stupid.
Australia is not a place of high social tension, or of high crime. Brisbane itself is a sunny, peaceful city with a normally benign river winding through the middle. When a disaster strikes, people are more likely to muck in and help out their less fortunate neighbours than to try and steal their stuff. Not that looting doesn't happen - some does, but there is plenty of incidents where citizens have interrupted looters and run them out of town.
Another feature of Brisbane flooding is that it affects rich and poor equally. Some of the most expensive houses front the river and have private pontoons (most of which are now in the ocean) - these get flooded. Some of the poorer areas are built in low-lying land, which also gets flooded. So it's not a class thing in that only the poor get affected. Some of the worst hit suburbs are also the most expensive suburbs to live.
As to why Australia tends to come together rather than fall apart - well, that would make for a fascinating social study. Personally I see it enshrined as part of the nations (and especially Queensland) culture - fair go, mateship, sticking together when the chips are down, having strength in adversity. You can probably explain as much when the most celebrated annual military parade day (Anzac day) commemorates Australia first and greatest military defeat, whereas there are no parades celebrating Australian military victories.
Or, to sum up even more succinctly, despite sharing a language and both being previous colonies, Australia and America are fundamentally different countries in many ways.