Welcome to AFF
@BaldyEagle . Qantas call centres are notoriously unreliable.
A Qantas Explorer seems like a good idea, but you will have to book your international ticket on Qantas, which could be more expensive than other options, maybe much more expensive, which could wipe out any savings from the domestic sectors. Being all on one ticket may also bring complications if you need to change?
Suggest you price the lowest fare international carrier to/from Australia that you'll fly on, then domestic sectors as individual tickets on Qantas and also Virgin Australia. Virgin tends to be cheaper and domestically there's not much difference, except for transcontinental, where Qantas sometimes run widebodies. Also Jetstar if you don't mind LCC. Of course you could mix them all up, choosing the best timings and fares for individual trips.
if you have status with OneWorld, that may tip the scales in favour of Qantas, as you may get lounge access and priority boarding etc, depending on your status level.
With 11 internal flights, you might look at joining Qantas Club if you go with Qantas (unless you intend to fly business, where QC isn't needed).