I dont know how it works in QLD so hopefully someone else can answer your question correctly...
If it was in vic, you wouldnt be able to as when you apply for a "Permit to Acquire", you would have to list a reason to why you want to own one. And because there isn't any approved "Airsoft playable" location (YET?!), they will not approve the "PTA".
Best to search the QLD police for more info. The VIC one is pretty decent for info regarding firearms so hopefully the QLD one is to.