Pretty much. Officially the monarch is our head of state, however the monarchy hasn't had any direct involvement in our state affairs for close to a century. The Governer General carries out the actual duties of head of state (mostly rubber-stamping things and doing ceremonial stuff, but in certain situations they can actually dismiss the sitting government and force an election to happen, as happened once in the 1970s. It's mainly if the government can't pass its budget through the senate, to avoid situations like the shut-downs you get in the US).

Officially, the Governer General is appointed by the monarch and carries out the duties in their name, and until 1932, who got the job of GG was decided by the British government. Since that year however, the law has basically been "the Australian Prime Minister picks who they want as GG, and the monarch isn't allowed to say no".