Your friend is fine with a Thai DL, you're not, however, as an Australian ID is not acceptable per CAAT ID rules - see below. If you've got photocopies of your passport with supporting documentation, you might get away with it, though - but it would be up to not just the airline, but airport security as well.
Also out of interest, when did handing over passports become a requirement to get a WP?
It's a proposal, nothing more or less, but unfortunately half of the Thai media were seemingly dropped on their heads as children and don't understand what a proposal is.