The first 24-48 hours are critical, and American news organizations tend to not want publicity, at least during that period. It can make it much more dangerous for her and difficult to secure her release.European news organizations often approach this issue differently, however, and will make an annoucement earlier, especially if they feel that the nationality of the reporter is likely to decrease the threat to his or her life. That is not the case here.
In the mean time if you want to know more about the incredible women who risk much to cover the war in Iraq have a look at the documentary Bearing Witness by Oscar-winner Barbara Kopple. Journalist Molly Bingham was actually taken prisoner and held at Abu Ghraib for a while by the Iraqis, and Kopple chronicles her return there along with several Iraqi women who shared her fate. These female reporters face incredible risks for often quite complex and compelling reasons and their commitment to telling the story always factors in this harrowing possibility.
Update: E&P: "A total of 76 journalists and media staff have been killed in Iraq since the U.S.-led invasion in March 2003, the press freedom group Reporters Without Borders said Wednesday. That was more than the 63 reporters killed in the 1955-1977 conflict in Vietnam, the group said, citing figures from U.S.-based press advocacy group Freedom Forum."