To meet next-generation IoT application demands, edge computing moves processing power and storage closer to the network edge to minimise latency and bandwidth utilisation. Edge computing is becoming popular as a result of these benefits, but resource management is still challenging. Researchers are utilising AI models to solve the challenge of resource management in edge computing systems. However, existing simulation tools are only concerned with typical resource management policies, not the adoption and implementation of AI models for resource management, especially. Consequently, researchers continue to face significant challenges, making it hard and time-consuming to use AI models when designing novel resource management policies for edge computing with existing simulation tools. To overcome these issues, we propose a lightweight Python-based toolkit called EdgeAISim for the simulation and modelling of AI models for designing resource management policies in edge computing environments. In EdgeAISim, we extended the basic components of the EdgeSimPy framework and developed new AI-based simulation models for task scheduling, energy management, service migration, network flow scheduling, and mobility support for edge computing environments. In EdgeAISim, we have utilised advanced AI models such as Multi-Armed Bandit with Upper Confidence Bound, Deep Q-Networks, Deep Q-Networks with Graphical Neural Network, and ActorCritic Network to optimize power usage while efficiently managing task migration within the edge computing environment. The performance of these proposed models of EdgeAISim is compared with the baseline, which uses a worst-fit algorithm-based resource management policy in different settings. Experimental results indicate that EdgeAISim exhibits a substantial reduction in power consumption, highlighting the compelling success of power optimization strategies in EdgeAISim.