I would not decide, the market would.
If there is a demand, they would come to the 'Coin Shop' and buy them, in as large or small a quantity as they like. Always at $1.
You have a job, and it pays you in these 'newcoins', then you go to your local coffee house and spend your coins, and then they spend the money they just made at your workplace, and the circle is complete..
You would not need to put more coins into the system for this transaction cycle to function.
As more people join the economy, there may not be enough Money in the system, so at that stage, they would go and buy some more coins from the Coin Shop.
That's what I like about it. The Money Supply would grow exactly as the economy requires it to.
Has a currency ever temporarily pegged itself to the USD ? And detached itself without disastrous consequences..?
There have been instances, such as the Zimbabwe hyperinflation in 2009, where locals give up their currency and start using dollars or Euros or others, and then transition onto a different national currency.
From the end of WWII until the 1970s USD was also exchangeable for gold so it was effectively "pegged" and any currency pegging to the dollar was also effectively pegging to gold. 1970 to today is basically uncharted waters, we will see how this global experiment plays out over the coming decade.
Addressing your example above, if I knew this was how the system operated and I were a speculator, what would prevent me from buying a large percentage of the coins and sitting on them until the billion has been sold and then make money from the rising price associated with growing demand and fixed supply?