Not to my knowledge Heather.
Do you have a specific island in mind? On Stradbroke the land would be prohibitively expensive, so your best bet would be Russell Island. If you're quick you could still get a nice block there close to the sea for under 20k. Re building the tiny home, I will 'cheer you on' all the way, and you will be able to get it done, but only if you have quite a bit of money and a FEW YEARS up your sleeve. Numerous reports indicate that the council is notoriously dysfunctional re the facilitation of timely builds of any kind, preferring instead to reap huge annual rate$ on EMPTY/unbuilt blocks of land. It makes sense, in a warped sort of way ... why actually take on the responsibility as a council of SERVICING OCCUPIED properties, when instead they can simply 'ETERNALLY SHADOW BOX ' with land-owners to the extent that they simply give up on the idea of building on their blocks--but continue to pay huge rates to the council--then sell their properties on to new owners who go on to do exactly the same thing ...
No matter how 'tiny' your home is, my understanding of the regulations on the islands is that you will need to install a septic tank system on your block, which will cost you 'quite a few grand' (someone in the business of septic tanks will be able to provide you with a more accurate estimation of the cost of this).
Lastly, If you decide to buy/build on Russell Island, don't fall for the 'council line' that you need to comply with any rules/regulations at all based on a premise that there are any koalas living on Russell Island. There are definitely NO KOALAS LIVING ON RUSSELL ISLAND, as any relevant scientific entity/authority based in Queensland will verify; and it is highly likely that no koalas have EVER lived on Russell Island.
Best of luck with your build :)