Text messages were sent out to Australians asking them to please download the app, which uses Bluetooth technology to keep track of interactions of more than 15 minutes with other people, on Monday.
But many Australians have expressed concerns over their privacy.
The federal government has promised to release the source code for the app, although this has not yet occurred.
The draft legislation for the app was released on Monday as the government works to ease anxieties on behalf of users.
Under the legislation, anyone who breaches the privacy safeguards of the app could face $63,000 in fines and up to five years imprisonment.
Neither your employer nor the government – or anyone else for that matter – can force you to download the app.
The same steep penalty may also be faced by businesses that try to refuse you entry if you have not downloaded the app.
The bill will also make it an offence to hold the data on a database outside Australia, following concerns about the use of global company Amazon Web Services’ servers.
The draft legislation – which still needs to be voted into law – also details who exactly is allowed access to the data and how long it can be kept before it must be wiped.