Whether your home-based food business needs a Food Safety Supervisor depends on the type of food it handles, not the fact that you operate from home. The requirement under Food Standard 3.2.2A applies to the food business activity, so trading from home does not, on its own, exempt you.
If your home-based business makes, handles or serves potentially hazardous, unpackaged food, it is likely to be a Category 1 or 2 food business and will need a Food Safety Supervisor available during its hours of operation. If you only handle low-risk or pre-packaged food, your business may not fall into these categories. You can check the full list in Which food businesses need a Food Safety Supervisor?
Home-based food businesses must also notify or register with their local council or state food authority before trading, and meet the same food safety requirements as any other food business.
If you are unsure whether your home-based business needs a Food Safety Supervisor, contact your local council or state or territory food authority.