Rothbard wants the dollar to be defined as a weight of gold. Under the Coinage Act of 1792, the dollar was defined as 247 4/8 grains of pure gold. In other words, the Treasury minted $10 gold coins each with 247 4/8 grains of pure gold. The dollar currency was a redemption claim for gold such that a person could take a $10 bill and redeem it for a $10 gold coin. Gold coins were money and currency was a redemption claim for money.
Defining the dollar was part of Congress’s power under the Constitution in Article 1, Section 8, Clause 5, which reads, “[Congress shall have the power] to coin money, regulate the value thereof, and of foreign coin, and fix the standard of weights and measures.” Just as Congress might adopt the mile as a standard of measure and define a mile as 5,280 feet, it might adopt gold as money and use the dollar as a currency name defined as $10 = 247 4/8 grains of pure gold.
Under this system, the market would determine the purchasing power of gold. But the name “dollar” is fixed by definition.