I think anyone can mine the goldcoins, and then redeem them at the exchanges for gold.
I don't think that's the OP's idea.
Why would any exchange back goldcoins with physical gold when anyone can mine for goldcoins? Exchanges like mtgox have traders on both the buy side and the sell side and that's how they come to the USD/BTC exchange rate. You don't just start an exchange and permanently set the exchange price yourself. If you do that, you will find that people will trade the worthless goldcoins to you for real gold and no one will trade away real gold for these goldcoins.
Only governments can really pull this off. That's because governments have a lot of gold, they have an incentive to make fiat currency successful, and they can force their citizens to pay tax in fiat currency. Tax forces people to have to trade in their gold for fiat currency. None of this is true for goldcoins.