That's half of the process. After you get your marriage license and complete the wedding formalities, which make the marriage legal in the US, you need to file a report with the Japanese consulate in New York (assuming you live in NYC) so that the marriage is recorded in Japan. Have your girlfriend read the attached link, which describes the Japanese legal process in more detail.
The Japanese consulate procedure is especially important for you, because if it is not completed, there will be no evidence of your marriage in Japan. This could cause you problems if you have a marital dispute down the road and your girlfriend goes back home.