You sponsor her for a UK PR visa
She sponsors you for a AU PR visa
Once all is processed you would be able to live and work in both countries. Please note PR visas do have residency requirements (at least in AU they do, check the UK one as well) so you need to spend enough time in both countries to maintain the PR status (this is an issue after the first 5 yrs as a PR in AU, please look into the topic of RRV - Resident Return Visa).
The only sure way to always have residency in both countries is to naturalise as Citizens (her as a UK citizen, you as an AU citizen). This is subject to the residency (physical presence as a PR) rules of each country.