Is There a Continent with a Single National Government?

No. There is no continent on Earth governed by a single national government.

Every continent comprises multiple sovereign states (countries), each with its own government, laws, and international recognition.

• Antarctica has no national government; it is governed internationally by the Antarctic Treaty System.
• Australia (the continent, sometimes called Oceania) includes the country of Australia, plus Papua New Guinea, New Zealand, and numerous Pacific island nations.
• Europe, Asia, Africa, North America, South America each contain dozens of independent countries.

The closest historical example might be a continent dominated by a single empire (e.g., the Roman Empire around the Mediterranean, or the Spanish Empire in South America), but these were imperial administrations, not a single "national government" in the modern sense of a nation-state.