When photographing hats for sale or display, choosing a proper background color is vital. You need a backdrop that enhances the hat, and that isn't so busy it distracts from it. A white hat against a white background can appear so washed out as to make it practically disappear. The same goes for a dark hat against a dark background. Experiment with different colored backgrounds and see what works best!
Here is an example of the same hat photographed against both a white and a black background. As you can see, the white background turns the white feather all but invisible. The black background not only makes the feather stand out, but makes all of the colors of the hat POP!