What is an Australian-style deal with the EU?
When the government talks about an Australian-style deal with the EU, it is talking exclusively about trade. The bulk of EU-Australia trade currently takes place according to World Trade Organisation (WTO) rules, meaning the imposition of many tariffs, quotas and customs formalities (albeit they are negotiating a free trade agreement to improve on them). If the UK does not reach a deal with the EU, UK-EU trade will then also be on WTO terms (Northern Ireland would be different).
However, in terms of the overall relationship – considering other issues such as security and wider political cooperation – a no deal Brexit would not lead to an Australian-style arrangement. The EU and Australia have built up a series of agreements over recent years, as well as being currently engaged in long-running negotiations over a future free trade agreement. The UK will have none of this if it leaves without an agreement.