Traffic Engineering (TE) has been applied to optimize network performance by routing/rerouting flows based on traffic loads and network topologies. To cope with network dynamics from emerging applications, it is essential to reroute flows more frequently than today's TE to maintain network performance. However, existing TE solutions may introduce considerable Quality of Service (QoS) degradation and service disruption since they do not take the potential negative impact of flow rerouting into account. In this paper, we apply a new QoS metric named network disturbance to gauge the impact of flow rerouting while optimizing network load balancing in backbone networks. To employ this metric in TE design, we propose a disturbance-aware TE called DATE, which uses Reinforcement Learning (RL) to intelligently select some critical flows between nodes for each traffic matrix and reroute them using Linear Programming (LP) to jointly optimize network performance and disturbance. DATE is equipped with a customized actor-critic architecture and Graph Neural Networks (GNNs) to handle dynamic traffic and single link failures. Extensive evaluations show that DATE can outperform state-of-the-art TE methods with close-to-optimal load balancing performance while effectively mitigating the 99th percentile network disturbance by up to 31.6%.