This study proposes a novel approach for dynamic load balancing in Software-Defined Networks (SDNs) using a Transformer-based Deep Q-Network (DQN). Traditional load balancing mechanisms, such as Round Robin (RR) and Weighted Round Robin (WRR), are static and often struggle to adapt to fluctuating traffic conditions, leading to inefficiencies in network performance. In contrast, SDNs offer centralized control and flexibility, providing an ideal platform for implementing machine learning-driven optimization strategies. The core of this research combines a Temporal Fusion Transformer (TFT) for accurate traffic prediction with a DQN model to perform real-time dynamic load balancing. The TFT model predicts future traffic loads, which the DQN uses as input, allowing it to make intelligent routing decisions that optimize throughput, minimize latency, and reduce packet loss. The proposed model was tested against RR and WRR in simulated environments with varying data rates, and the results demonstrate significant improvements in network performance. For the 500MB data rate, the DQN model achieved an average throughput of 0.275 compared to 0.202 and 0.205 for RR and WRR, respectively. Additionally, the DQN recorded lower average latency and packet loss. In the 1000MB simulation, the DQN model outperformed the traditional methods in throughput, latency, and packet loss, reinforcing its effectiveness in managing network loads dynamically. This research presents an important step towards enhancing network performance through the integration of machine learning models within SDNs, potentially paving the way for more adaptive, intelligent network management systems.