I liked this chart because it gives you a very rough idea of how many hours of storage is needed. Looking at it from the net demand side, you'd need storage from about 16:00 to about 1:30. The peak after midnight is prolly from water heaters, which were programmed to turn on after midnight in the days when all power was produced by baseload generators. Those timers should be shifted to midday. So that suggests (in the absence of wind) that we need 8 or 9 hours of storage. Looking at it from the supply side, we'd need enough storage to store electricity from 6:30 to 16:00, which is 11 to 12 hours.
The new Tesla Powerwall will store 14 kWh. Average annual electricity use by households in Queensland is 5793 kWh, or 16 kWh a day. That means that one Powerwall battery should almost cover net demand from 16:00 to 6:00. I keep on meaning to do a proper estimate of the Powerwall's LCOE, but a rough and ready guess would be AU 13.6 cents/kWh (=A$10,500 including GST and installation, divided by 14 kWh*365 days*15 years) Now my electricity retailer, here in Victoria, charges AU 28.5 cents per kWh., including GST. I imagine costs in Queensland aren't that different. Which means that it makes sense if you already have solar panels to install a Powerwall battery "behind the meter". And as behind the meter storage becomes more common, the "peaking duck curve" will flatten.