IF - and it's a fair sized 'if' ----- if it's allergens from the dog that are upsetting you
the allergens from dogs are proteins in their saliva, urine and dander
when they shed, dander etc which is on their fur spreads though the house
no magic washes are required ------------- brush and get rid of loose fur daily, wear a mask - put the loose fur in the bin rather than the dog putting it on the carpet or the bed.
that would be the first thing. Washing is a double edged sword - washing is not good for dog's skin. So the occasional wash is fine, maybe once a week IF there's an allergy issue (normally less if no issue) with something mild, but if one does it too often, the dog's skin gets stirred up and likely flakes more - meaning more dander.
I'd also make sure that there's no mould about - I understand Townsville is normally dry - but, you've had some pretty wet and hot spells.
Also - dust. Dust, dust dust - can cause problems as well.
If you want to test to see if the dog is the problem ----------- isolate and clean a room and keep fido out of it - a dog free zone ----------- then, spend some time in there when you have clean clothes on - and see if there's a difference.