Quality Estimation (QE) aims to assess machine translation quality without reference translations, but recent studies have shown that existing QE models exhibit systematic gender bias. In particular, they tend to favor masculine realizations in gender-ambiguous contexts and may assign higher scores to gender-misaligned translations even when gender is explicitly specified. To address these issues, we propose FairQE, a multi-agent-based, fairness-aware QE framework that mitigates gender bias in both gender-ambiguous and gender-explicit scenarios. FairQE detects gender cues, generates gender-flipped translation variants, and combines conventional QE scores with LLM-based bias-mitigating reasoning through a dynamic bias-aware aggregation mechanism. This design preserves the strengths of existing QE models while calibrating their gender-related biases in a plug-and-play manner. Extensive experiments across multiple gender bias evaluation settings demonstrate that FairQE consistently improves gender fairness over strong QE baselines. Moreover, under MQM-based meta-evaluation following the WMT 2023 Metrics Shared Task, FairQE achieves competitive or improved general QE performance. These results show that gender bias in QE can be effectively mitigated without sacrificing evaluation accuracy, enabling fairer and more reliable translation evaluation.