With climate change insects move geographically. New regions open up to be populated. Warming of the Australian mainland has taken place. The Asian tiger mosquito has been found on Thursday and Horn islands in the Torres strait close to Australia itself.
Dengue and chicungunya are the greatest dangers. These diseases can be fatal. There is no way the mosquitoes can be stopped. They will move into Australia proper. Spraying insecticides will only slow them down. They won't fly to Australia. They will be brought here on small boats moving all over the Torres Strait.
The threat is serious. Once established in Australia Asian tiger mosquitoes will be spread by humans as far south as Tasmania. They prefer a cooler climate than the main dengue host, Aedes aegypti. Tigers will carry dengue, however.
The outside-life of Australians is under threat. Having a barbecue will be a dangerous pastime. Recently it has been established that mosquitoes are not native to Papua New Guinea. They came from Indonesia, so migration is normal for the insect.