This paper studies the distributed dynamic event-triggered model predictive control (MPC) of vehicle platoon systems subject to denial-of-service (DoS) attacks and external disturbances. We develop a novel DoS-attack-aware event-triggered mechanism for each vehicle to determine whether the MPC problem should be solved or not at each sampling time instant. If the MPC problem is solved, the constructed vehicular beacon information will be transmitted to its neighbouring vehicles through the vehicular ad-hoc network (VANET). In the DoS-attack-aware event-triggered condition, the dynamic threshold adjusts adaptively according to DoS attack durations, local vehicular data, and beacon information from its neighbours. Then, an exponential-type robustness constraint is introduced in the MPC problem to deal with external disturbances. Subsequently, sufficient conditions are given to guarantee the recursive feasibility of the MPC algorithm and closed-loop platoon system stability. Finally, extensive simulation examples are provided to illustrate the effectiveness of the proposed algorithm in terms of communication efficiency and platoon resilience control performance.