Let's just say I doubt it. Inflation only occurs if the money supply increases relative to the supply of available goods and services. Rothbard couldn't possibly posit a fixed supply of gold as there has never been a time in recorded human history where the total gold owned throughout the world didn't increase from one year to the next.
Go back and read what he wrote.
ML/NJ
I didn’t say that Rothbard posited a fixed supply of money. I said “Rothbard (Austrian School of Economics) define inflation as any increase, from any source including new found gold, in the money supply. The fixed supply of gold is why they find it so attractive as ‘money’.”
“What happens, then, if the supply of gold increases, demand for money remaining the same? The “price of money” falls, i.e., the purchasing power of the money-unit will fall all along the line. An ounce of gold will now be worth less than 100 loaves of bread, 1/3 of a television set, etc. Conversely, if the supply of gold falls, the purchasing power of the gold-ounce rises.” Rothbard.
http://www.mises.org/money/2s8.asp
BTW, Rothbard also said (Same article): “Changes in the total gold stock will be governed by the same causes as changes in other goods. Increases will stem from greater production from mines; decreases from being used up in wear and tear, in industry, etc. Because the market will choose a durable commodity as money, and because money is not used up at the rate of other commodities?but is employed as a medium of exchange?the proportion of new annual production to its total stock will tend to be quite small. Changes in total gold stock, then, generally take place very slowly.”
Please note the phrase “Changes in total gold stock, then, generally take place very slowly.”