The capital of Australia is

A country's capital is the city officially designated as the seat of its national government — its parliament, head of state, and central administrative offices. This official status is independent of a city's population, economic weight, or historical importance; a country's largest or oldest city need not be its capital.

Australia's capital is Canberra. After the six colonies federated in 1901, Sydney and Melbourne — the two largest, most prominent cities — both wanted the honour, so as a compromise, a new capital city was planned and built between them, inside the Australian Capital Territory. Melbourne hosted the Federal Parliament temporarily from 1901 until Canberra's Provisional Parliament House opened in 1927, after which Canberra became the official, permanent seat of the Australian government; the current Parliament House later replaced the provisional building in 1988.

Checking each option against this:

• Melbourne — hosted Parliament only as an interim measure before Canberra was ready; it was never legislated as the permanent capital.

• Sydney — Australia's largest and best-known city, but it has never held the status of national capital.

• None of these — does not apply here, since the actual capital of Australia is one of the cities already listed among the options.

Hence, the capital of Australia is Canberra.