The Short answer here is – yes. The action of vaping is not banned or outlawed in any state or territory in Australia. There are the usual excusion zones in certain areas such as no smoking areas, as some states do not provide split legislation for smoking and vaping. We recommend that you look into the state and federal laws that allpy to you specificly in your place of residence.
Most of the confusion with vaping being legal/illegal comes from the lack of clarity surrounding the legality of liquid nicotine, not the act of vaping itself. Here is a handy link to Legalise Vaping Australias site that has an up to date table on the laws state by state surrounding this if you would like some more indepth information.