It all relies on which part of Queensland you're in. I'm in Brisbane myself, just a short drive out of the CBD, where stores, pharmacies and various brands are fairly abundant. Whilst out in more regional/remote areas you'll have a tough time finding anything [decent].
For starters, just to get it out of the way, there's Depends. Pretty much every pharmacy carries them and some supermarkets too. Obviously the quality is lacking quite a bit, but nonetheless a reasonable diaper with high availability. On this same note, there's another brand that's been in stock recently called MoliMed (can spot them easily, they come in a sunflower-yellow packet). Despite being made by the same company as Molicare (Hartmann), I've heard these are pretty generic diapers. Avoid, if possible, although keep in mind I haven't personally tried them, so this is just what I've heard on the grapevine. However, I haven't heard anything largely negative about them.
**Note: I just checked the website. MoliMed's don't appear to come in a brief-style, tape-up pad. So I wouldn't worry about them.
Lately, a few of the premium brands, like Tena and Molicare (I'm talking about the proper tape-up kind, not the pull-up kind), have been showing up in a handful of pharmacies around my area, and I think one in the city as well. They're more expensive, but well worth it if you can find any. Just to note, we get the European version of the Tena Slip Maxi, not the apparently worse-off US variety - they are some of the best diapers from any brand, so if you find some I'd definitely recommend buying a pack or two.
If searching around isn't your thing, then you could always try businesses that deal with incontinence supplies. I know for sure that Sanicare, Abena's kid company that operates in Australia, has offices around the major cities. You can check their
most recent catalogue here and their
office locations here. I believe you can phone order, but I'm not entirely sure if the offices themselves have stock on hand, but I'm sure you can ask. Hartmann and Tena also have Aussie websites if you want to look them up.
Alternatively, and I know you didn't say you wanted to online order, but there are a couple of sites that are half-decent to order from -
BrightSky and
Independence Solutions are one's I've dealt with before and they aren't half-bad; quick shipping for the metro areas. Also, I think they have warehouses you can visit and buy direct from, but don't quote me on that.
And lastly, there's a special site from a Brisbane-local who makes her own Velcro cloth diapers... and she does adult sizes too!
Check it out here.