Slicing-enabled communication networks refer to a network architecture that enables the definition of multiple virtual networks or "slices" over a shared physical network. Each slice operates independently with its own dedicated resources, configuration, and management. However, this poses a major challenge in guaranteeing optimal resource allocation among those slices while preserving the obligatory Quality of Service (QoS) levels for each one. This study presents a federated learning-driven digital twin (DT) framework named FED-DT for creating a digital replica of the physical slicing-supported network to mimic its complicated infrastructure and forecast the network's dynamic performance. In FED-DT, the DT of network slicing is designated as non-Euclidean graph representations. A novel lightweight Graph Lineformer Network (GLN) is introduced to collaboratively learn and estimate QoS metrics from the topological structures of the underlying network slices. The FEDDT is empowered with an intelligent self-supervision method to improve generalizability on a large network, while Gaussian Differential Privacy (DP) is applied to guarantee the preservation of model privacy during training. Proof-of-concept simulations on different network topologies demonstrate the effectiveness of FED-DT in fulfilling rigid QoS requirements and achieving ideal performance.