Avatars, as promising digital assistants in Vehicular Metaverses, can enable drivers and passengers to immerse in 3D virtual spaces, serving as a practical emerging example of Artificial Intelligence of Things (AIoT) in intelligent vehicular environments. The immersive experience is achieved through seamless human-avatar interaction, e.g., augmented reality navigation, which requires intensive resources that are inefficient and impractical to process on intelligent vehicles locally. Fortunately, offloading avatar tasks to RoadSide Units (RSUs) or cloud servers for remote execution can effectively reduce resource consumption. However, the high mobility of vehicles, the dynamic workload of RSUs, and the heterogeneity of RSUs pose novel challenges to making avatar migration decisions. To address these challenges, in this paper, we propose a dynamic migration framework for avatar tasks based on real-time trajectory prediction and Multi-Agent Deep Reinforcement Learning (MADRL). Specifically, we propose a model to predict the future trajectories of intelligent vehicles based on their historical data, indicating the future workloads of RSUs.Based on the expected workloads of RSUs, we formulate the avatar task migration problem as a long-term mixed integer programming problem. To tackle this problem efficiently, the problem is transformed into a Partially Observable Markov Decision Process (POMDP) and solved by multiple DRL agents with hybrid continuous and discrete actions in decentralized. Numerical results demonstrate that our proposed algorithm can effectively reduce the latency of executing avatar tasks by around 25% without prediction and 30% with prediction and enhance user immersive experiences in the AIoT-enabled Vehicular Metaverse (AeVeM).