Traveling with my pet - German Shepherd?

Will be going from Upstate NY to Southern California via American Airlines with my German Shepherd. Plain will go from NY to Chicago (2 hours) and then Chicago to California. My pet will have to be in cargo in a crate. Question is... has anyone done this? How risky is it? We'll be traveling this month. I have heard some crazy stories of dogs dieing, and now I'm very nervous about trying to remain calm on a flight without knowing whether or not my dog is comfortable or not. How much of a risk is involved with this?