It appears you may be able to apply for Suncorp cover as the Insurer is AAI Ltd a wholly owned subsiduary of Suncorp (AAI Limited ABN 48 005 297 807 AFSL No. 230859 trading as Suncorp Insurance). You could try their online quote system. I used a Melbourne postcode and address to start the process and it did not decline the address even though it is out of Qld.
https://online.suncorp.com.au/home/pub/sunquote?execution=e1s1
