Do I need to buy my own router for NBN?

In most cases, yes — the free routers some ISPs include are usually basic and underpowered. NBN Co (or your building, on FTTB/Opticomm) already provides the connection box; you generally only need to buy a router that supports PPPoE. A solid mid-range WiFi 6 router is a worthwhile investment for most households sharing an apartment.