If you move to the UK before the end of the transition period (which is now planned to coincide with the end of this year), you and your spouse will be able to register for the EU settlement scheme. It is free of charge and relatively quick and easy, and citizens of Australia and of the US (among other countries) do not need to apply for a family permit before moving to the UK.
If you move after the end of the transition period, then your spouse will have to apply for a spouse visa. The path from spouse visa to ILR costs several thousand pounds over a few years. It is not nearly as straightforward as the settlement scheme. Among other burdens, you must show that you meet the financial requirements.