This paper develops a nonlinear output-feedback controller to force a non-minimum phase, underactuated vertical take-off and landing (VTOL) aircraft to globally asymptotically track a reference trajectory generated by a reference model. The control development is based on a global exponential observer, some global coordinate transformations, Lyapunov's direct method and the popular backstepping technique. In addition, it is shown that our control design scheme can be extended to the case of control input saturation. Interestingly, the proposed methodology also yields new results for the previously studied problems of stabilization and output tracking or regulation. Numerical simulations illustrate the effectiveness of the proposed controller.