Queensland is a big place. Where are you planning to travel?
Some travellers come here, buy a car and some gear, then sell it all at the end of the trip. Would that suit you? In that case, I would suggest starting in Brisbane, where there would be the best range of equipment available.
Hiring gear is not so simple. There are just not the same kind of massive hire spots in Australia that you see in Europe. Although there are many good sailing spots on the Sunshine Coast (where I live) I can only think of one, maybe two, hire places, and their range is probably better suited to recreational sailors.
I don't know if shops here are set up to do extended hire. Perhaps someone with first hand knowledge can help out here? I know lots of shop people lurk around here.
As for sailing venues, I assume since you are from Switzerland that you are used to sailing on lakes, perhaps in the Mediterranean. Ocean sailing here is hard for some European sailors, so you may want to stick to lakes and estuaries. Flatter spots like those preferred by the GPS Team Chellenge sailors will suit European sailors better.
Wellington Point, Golden Beach, Gold Coast (the Train), Lake Cootharaba, all fairly good for people used to flatter waters.
Always make sure you sail where other people are sailing, and ask for advice about local spots from local sailors, because you need to know about potential dangers. (For instance, Golden Beach is pretty safe, but float around the corner to Bulcock Beach and you may well end up being rescued and/or losing your gear.)
Good luck! Safe travels. And watch out for the drop-bears.

Dylan.