Because of their attractive economic and environmental benefits, integrated energy systems (IESs), especially electricity-gas coupled energy systems (EGCESs), have received great interest. In this study, to minimize carbon trading and generation costs, a model-free deep-reinforcement-learning (DRL) method is integrated into the low-carbon economic autonomous energy management system of an EGCES. Unlike previous works, this work proposes an innovative transformer-deep deterministic policy gradient (TDDPG) that combines the superior feature extraction ability of the transformer network with the strong decision-making ability of a state-of-the-art TDDPG. The proposed method is tailored to the specific energy management problem to meet the requirements of multi-dimensional and continuous control. To validate the advantages of the TDDPG, the proposed method is compared with benchmark optimization methods. The simulation results illustrate that TDDPG performs more effectively than the examined DRL approaches in terms of optimizing low-carbon and economy targets, computation efficiency, and optimization of the results. Besides, the TDDPG method achieves lower average comprehensive costs than DDPG and requires less training time for real-time energy scheduling.