Mixture of Experts (MoE) models have achieved great success by significantly improving performance while maintaining computational efficiency through sparse expert activation. However, their enormous parameter sizes and memory demands pose major challenges for deployment in resource-constrained environments. Vector Quantization (VQ) offers a promising approach for ultra-low-bit compression in Large Language Models (LLMs) by leveraging a codebook, where weight vectors are mapped to the most similar discrete codewords. Yet, directly applying VQ to MoEs often leads to substantial performance degradation due to two critical obstacles: (1) redundant representations among experts cause VQ to repeatedly quantize similar representations for each expert, resulting in inefficient use of limited codebook capacity; and (2) cumulative output bias is amplified by expert aggregation in MoE layers, leading to distributional shifts in the quantized outputs. To address these issues, we propose KBVQ-MoE, a novel VQ framework to enhance extremely low-bit quantization for MoE-based LLMs. KBVQ-MoE integrates two techniques: (1) input-driven redundancy elimination, where a Karhunen-Loeve Transform (KLT) guided singular value decomposition (SVD) extracts dominant weight components and shares them across experts; and (2) bias-corrected output stabilization, where vector quantization is applied only to expert-specific (non-redundant) representations and the quantized outputs are corrected via channel-wise affine compensation. Experiments on various MoE LLMs demonstrate that KBVQ-MoE preserves accuracy substantially better than existing quantization methods. For example, 3-bit quantization of Qwen1.5-MoE-A2.7B achieves an average accuracy of 67.99, nearly identical to the FP16 baseline of 68.07, underscoring KBVQ-MoE's potential for efficient deployment on edge devices and other resource-constrained platforms.