In this study, trajectory planning and control of a cable-suspended load from a quadrotor in a special transportation mission are addressed. The mission under consideration in this study includes picking up and transportation of the load toward a defined point at a specified time. Therefore, two trajectory tracking controllers are designed for the quadrotor and the load. Controllers are designed geometrically via Backstepping and configuration error functions defined on S2 and SO(3) in the literature of Lie groups. By this way, common singularities of regular quadrotor attitude controllers are avoided. Moreover, sufficient conditions for success of the proposed control laws are calculated using Lyapunov exponential stability theorem and an argument about singularly perturbed systems. All simulations are performed on an experimentally verified model of OS4 quadrotor and capabilities of the designed control laws are demonstrated.