Wam, you can certainly have solar, and solar + battery, and be on the Night Saver EV plan.
It's an awesome plan, allowing you to charge for 6 hours 0000-0600 for 8c a kwh.
We have 2 EVs here now and are putting in 12kw to 14kw into those and the HWS / overnight trickle to home for several hours during that time, having one on the 7kw charger, and the other more lightly used on the 10amp / 2kw granny charger.
All power into the home in that 6 hours is charged at 8c.
What we pay for charging on the plan is a fraction compared to old petrol cost, roughly $2 / 100km vs previous Elantra (we still have for now) $14 / 100km average here in Adelaide.
Put your address in here and see the plan with local rates for other times, and your daily supply charge.
https://www.agl.com.au/residential/energy/compare-plans/night-saver-ev-plan
The bonus is you can top off your EV during the day free from solar too, if you need this, but depending on usage patterns, it's cheap either way.
You will have to wait until you get your EV rego, when you apply you enter your vehicle rego number.