This dataset is only a list of local govt areas, so you'd need to merge it with the boundary data for those LGAs, but might be usable?
https://data.gov.au/data/dataset/dcp-lgas
Also the instructions here suggest that at least some level of data is exportable from here:
https://map.drought.gov.au/help.html
"How to download data from the map
There are two types of download:
- Raw data: Once a dataset has been selected, click the "About this data" button, then scroll down to the Data URL and click on the link. Data download depends entirely on custodians making it available. Should the raw files not be available, users need to contact custodians directly; their details are available under Data Custodian or Service Contact, on the same page.
- Feature Information: Once a point or a polygon on the map is selected and the Feature Information window is shown, you can download the data in that particular feature info window, by scrolling down and clicking on Download this Table, in CSV or JSON. It will just download the feature info table, not the actual, raw data."
Hope that helps!