A nice piece appeared on the ABC website here.
La Nina is the opposite of El Nino. It occurs when the sea surface temperatures in the western Pacific/Coral Sea are warmer than usual and the winds across the Pacific are stronger than usual. A measure of the strength of this circulation is the Southern Oscillation Index or SOI, which is a measure of pressure differences across the Pacific. Pressure differences are related to temperature differences and hence produce differences in the win strength. Apparently it was 27.1 in December, the highest ever measured. Hence, while floods and Tropical Cyclones like those observed have occurred before, the conditions that have caused them appear to be unusual.
Dr Andrew Ash of the CSIRO suggests part of this is due to global warming, producing the lower than usual pressures over the western Pacific. This reinforces the idea that flooding and strong TCs are expected to increase in frequency under human-induced global warming, even if the mean trend is drying in our part of the world.