First, the price of all goods that we export is not dictated by us, that is, our country is a price taker and not a price maker. Therefore, your proposal is equivalent to a mining tax imposed upon our gold producers, something against which the mums and dads holding shares in mining companies would object.
Second, a gold backing currency refers to a monetary policy in which a currency is based on a quantity of gold The government issuing the currency ties its value to the amount of gold it possesses, hence the desire for gold reserves. This means that our dollar would be up and down in response to variations in the price of gold and most likely neither our exporters nor importers nor our central bank [a bastion of price stability] would like that.
A curious aspect about the pricing of an exhaustive commodity [gold].
