Although many seem to believe that it is illegal to bring drumsticks on a plane, according to Transport Security Administration, the agency that oversees the security of public traveling in the US, it is, in fact, legal to take your drumsticks with you while traveling by plane.
However, just like any other musical instrument, including parts of instruments, such as a delay pedal, you have to inform a TSA officer about the fact that you are carrying such an item with you. Furthermore, according to the TSA, it is necessary that all brass instruments are packed in the checked bags.