Yes you may. Service Stations and Move Yourself will remain open during a lockdown.
See below link to the Australian Government Department of Health website which list’s what we can and cannot do during
a lockdown. From previous lockdowns our experience has been yes it is allowed, providing you meet the requirements as
per directed in terms of social distance and mask wearing etc.
There are also links within the health.gov website that takes you to your local state Health website for state specific requirements.
We don’t recommend crossing borders if the state you're travelling to is in lockdown, or the state you're travelling from is in lockdown. If it’s a one way booking and you're moving house, then this is ok, just ensure you have checked your local government Covid-19 permit requirements if any, before you pick up the booking.