National Parks in Australia are managed by individual state. Here are the links to each state's national park website. It is very important to check before you visit the parks as some parks may be closed due to weather condition. For example, after the bushfire, some parks were closed for a long time to allow for revegetaion.
For camping at popular places such as Wilson Promontory in Victoria during peak season, you need to book early. For Christmas summer holiday, you need to apply in June via a ballot system.
NSW National Parks
Victoria National Parks
Queensland National Parks
South Australia National Parks
Western Australia National Parks
Tasmania National Parks
Northern Territory National Parks
Australian Capital Territory National Parks (ACT - Canberra)