Stingers are found in all tropical waters at all times of year in all parts of the world but they tend to be much more prevalent in the warmer months. When the water temp gets over 27C and the northerly winds kick in, their numbers tend to go up - but it is very seasonal and no-one has worked out as yet how to predict a good or bad season. So far this season it's been quiet (the water temp is cooler than usual) but I'd expect reports of box jellyfish on the coastal fringe by the end of November. Please note that deadly jellyfish exist on the outer reef as well as the inshore islands and beaches.
Airlie "Beach" is actually a mud flat so you won't be tempted to swim in the ocean. However, they have a fabulous man-made lagoon which is a great spot to spend time - right in the centre of the town. Once you get out on the islands or on a boat, you really should talk to the people responsible for your safety. Good operators will recommend stinger suits for all swimming and diving at that time of year. This will reduce your personal risk sunstantially.
Great part of the world at a great time of year. Enjoy.