Both the Mobile edge computing (MEC)-based and fog computing (FC)-aided Internet of Vehicles (IoV) constitute promising paradigms of meeting the demands of low-latency pervasive computing. To this end, we construct a dynamic NOMA-based computation offloading scheme for vehicular platoons on highways, where the vehicles can offload their computing tasks to other platoon members. To cope with the rapidly fluctuating channel quality, we divide the timeline into successive time slots according to the channel's coherence time. Robust computing and offloading decisions are made for each time slot after taking the channel estimation errors into account. Considering a certain time slot, we first analytically characterize both the locally computed source data and the offloaded source data as well as the energy consumption of every vehicle in the platoons. We then formulate the problem of minimizing the long-term maximum task queue by optimizing the allocation of both the communication and computing resources. To solve the problem formulated, we design an online algorithm based on the classic Lyapunov optimization method and successive convex approximation (SCA) method. Finally, the numerical simulation results characterize the performance of our algorithm and demonstrate its advantages both over the local computing scheme and the orthogonal multiple access (OMA)-based offloading scheme.