I have a competing back of the envelope calc...
Australia electricity generation in 2016/17: 258,017GWh
see Table O
https://www.energy.gov.au/publications/australian-energy-update-2018Installed capacity ~50GW or ~48GW if you take out the announced closures... (see
https://www.aemo.com.au/Electricity/National-Electricity-Market-NEM/Planning-and-forecasting/Generation-information) the question is how much electricity can be generated in a year with installed capacity of X. It depends on utilisation, which is affected by maintenance, disruptions, and in the case of renewables, the variability of the weather. At 100% utilisation 365/24/7, it's about 420,000GWh @48GW, which is the absolute upper bound.
The back of the envelope suggests not quite enough capacity, but it obviously ignores a few complications, one of which is that ICEs don't convert the contained energy of petrol very efficiently (I think I've seen 25%?), while electric motors are somewhat better at converting the contained energy of a battery into movement (50%?). If it's 50%, then you'd only need half (25/50) of the contained energy of petrol to move you the same distance in a car, which would reduce the energy required from 177TWh to a number closer to 90TWh. Still a large increase relative to generation of 258TWh.
Back of the envelope calcs like this and
@mecad's one are useful to get a sense of scale, but they definitely leave a lot of detail out and may also be missing some really important crucial element. Fortunately 100% saturation with EVs is not going to happen for quite a while, but I'm sure some real planning is going into looking at the long term path for capacity.