The Telecommunications (Interception and Access) Amendment (Data Retention) Act 2015 requires telecommunications companies to retain a particular set of telecommunications data for at least two years to ensure Australia’s law enforcement and security agencies are lawfully able to access these data.
However, the law does not require internet service providers, like TPG, to retain a person's web-browsing history or any data that would amount to web-browsing history.
Refer to Paragraph 187A(4)(b) of the law.
Many browsers keep a history of sites visited.
If you want to keep see which sites have been visited by different computers on your home network you could look at the browser histories on each computer or alternatively, set up a proxy server. Apparently you can create one for free with google. Or you could buy a cheap computer like a Raspberry Pi and configure it to work as a proxy server or a firewall.