While it's correct that you often automatically become tax resident (and liable on taxes on your worldwide income) after ~183 days in a country, you may very well become tax resident well before that due to other triggers. More information for Australia is available here.
Australia also tax temporary residents (typically people on a working holiday visa) on their locally sourced income (meaning for work performed in Australia—so technically including remote work, but in practice I wouldn't worry about it). As of Jan 1, 2017 temporary residents pay a flat tax of 19% on their income up to AUD 37,000 and regular tax rates thereafter.
Bottom line is, as long as you're not on a working holiday visa and do what @international_man said above, you'll be fine. Whether you rent a desk at a coworking space or work from your apartment is not likely to affect your tax liabilities to Australia.
Disclaimer: This is in no way legal or tax advice. Don't believe anything I just said, or anything else you read online.