Why not just adopt Bitcoin itself as a main currency? You could even set up a fractional banking system based on top Bitcoin. The first government to do this is going to have a huge economic advantage for the rest of this century.
You know, it's REALLY difficult to do FRB with Bitcoin, since you are REALLY relying on having more people funneling in Bitcoins. And guess what happens when some-one wants to withdraw? Either you start funneling Bitcoins out of other's accounts, and they're left with the IOUs. And what happens when they want to withdraw, etc. It's possible, but difficult.
That's why wallets were made, so people can be their own bank. And not have to go through the bureaucracy that comes with banks. And they can't be left with IOUs, ever. Either a Bitcoin is there or it's not.
If you can do FRB w gold you can do it w bitcoins. The difference is if people have wallets then they dont need to keep their deposits in a bank.
But loans would still exist and credit money would still exist. Banks dont really need deposit accounts these days to create loans.
For example if you lease a car, the leasing bank creates credit without any deposit accounts