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Economic and policy factors are driving the continuous increase in the adoption and usage of electrical vehicles (EVs). However, despite being a cleaner alternative to combustion engine vehicles, EVs have negative impacts on the lifespan of microgrid equipment and energy balance due to increased power demands and the timing of their usage. In our view, grid management should leverage on EV scheduling flexibility to support local network balancing through active participation in demand response programs. In this paper, we propose a model-free solution, leveraging deep Q-learning to schedule the charging and discharging activities of EVs within a microgrid to align with a target energy profile provided by the distribution system operator. We adapted the Bellman equation to assess the value of a state based on specific rewards for EV scheduling actions and used a neural network to estimate Q-values for available actions and the epsilon-greedy algorithm to balance exploitation and exploration to meet the target energy profile. The results are promising, showing the effectiveness of the proposed solution in scheduling the charging and discharging actions for a fleet of 30 EVs to align with the target energy profile in demand response programs, achieving a Pearson coefficient of 0.99. This solution also demonstrates a high degree of adaptability in effectively managing scheduling situations for EVs that involve dynamicity, influenced by various state-of-charge distributions and e-mobility features. Adaptability is achieved solely through learning from data without requiring prior knowledge, configurations, or fine-tuning.