The Murray used to run dry before they diverted the Snowy, e.g. 1915. This is going to happen whether we "fix" global warming or not [of course running out of fossil fuel will fix it, ice age to follow]. Australian food production is good on average over time and/or space. We need a system where farming activity can move around more, and we need more food storage. Hell, the world needs more food storage: with no reserves we are just waiting for a big volcano or monsoon failure or something and we'll have 100 Ethiopias running at once.

Robert,as you say,Australia has always had a wildly variable rainfall over most of the continent.This may well get a lot worse in some areas, with climate change.The science is uncertain about the location and extent.We also have to factor in the widespread degradation of agricultural areas due to past(and present) soil mining practices.Salinity is another growing problem.
The most urgent issue is the role of fossil fuels in agriculture.Cereal crops are almost all broad acre dryland farming.Even with minimum tillage methods the cost of diesel will rapidly push a lot farmers into bankruptcy given the high level of debt that they normally carry.
There is some risk that Australia could largely cease to be a grain exporter and the worst case scenario would be a domestic food crisis.
In keeping with the present blind leading the blind style of governance in Australia I have seen very little discussion about the points raised above let alone any attempt to address them.