The size of an economy is a very important measure, and also a measure that is very hard to define.
Now, we want to measure the size of the Bitcoin economy. I didn't see any GDP numbers for Bitcoins. It will be very hard to collect the raw data necessary to calculate the Bitcoin GDP. Since Bitcoin is a global phenomena, the Domestic part means actually all the world. Also, a lot of Bitcoin transactions are probably an exchange for non-legal economic value with the intent of not leaving an official trace.
But, one advantage of Bitcoin is the fact that every transaction is actually transparently recorded in the blockchain and every one, not only govenrment officials, can go and mine the blockchain to gain insight.
So, we can come up with two limits to the size of the Bitcoin economy. In the lower limit we can observe how much the current money base of Bitcoins is worth. The calculation is very simple: multiply current number of Bitcoins with the current exchange rate. You can see the number calculated in the Bitcoincharts website. In this site it is called Market Cap and currently it is estimated as 127,440,489 USD. This is obviously not a big number, and it represents the vulnerability of the Bitcoin economy against a large attack from the current economic forces (namely, big corporations and banks).
The upper limit will be more realistic to the actual size of the economy. We can calculate it by multiplying the amount of Bitcoins sent during a time period with the current exchange rate. By this account, the size of the Bitcoin economy in 2012 was 785,558 trillion USD. I took the number of Bitcoin sent (according to the State of the Coin 2012 presentation) and multiplied it by current mtgox exchange rate. This is too large number to believe and I think there is an error in the presentation. Another way of estimating this number is by the following formula: <daily Bitcoins sent>*365*<exchange rate>. Taking the number of daily Bitcoins sent from Bitcoincharts we get 5.7 billion USD yearly Bitcoin economy size. This number is still large, but it makes sense.
The upper limit includes transactions which transfer Bitcoins between addresses of the same economic entity. The volume of these "internal" transactions can be very high and it is quite problematic to remove them from the economy size estimation. In the Bitcoin community there is a measure which is called Bitcoin Days Destroyed. This measure is calculated by taking the number of Bitcoins in a transaction and multiplying it by the number of days it has been since those coins were last spent. Bitcoin Days Destroyed attempts to provide a reliable indication of transaction volume that strips out transfers to oneself and immediate account reorganizations. I don't think this measure attempt is very successful. But maybe the Bitcoin community will find improvements to these kind of measure and we will have a better way to estimate the Bitcoin economy.
So, my best guess at the size of the Bitcoin economy is several billion USD. This is quite large, but it is still nothing compares to the world economy.