Quantum cloud platforms have scaled hardware capacity but not the abstraction exposed to users: small programs still monopolise entire processors, and existing Quantum Virtual Machine (QVM) designs often rely on fixed, topology-specific partitions that are brittle under calibration drift, spatial heterogeneity, and transient defects. We present DynQ, a dynamic topology-agnostic QVM that derives execution regions directly from live calibration data. DynQ models a processor as a quality-weighted coupling graph and formulates region discovery as community detection, turning high internal cohesion and low external coupling into a hardware-aware objective for quantum virtualisation. This produces regions that are compilation-friendly, quality-aware, and resilient to degraded couplers and unavailable qubits. DynQ separates offline region discovery from online allocation, enabling low-latency scheduling over pre-validated regions while allowing recomputation under changing hardware conditions. Across five IBM backends, real-device experiments on IBM Kingston and Torino, and cross-architecture evaluation on Rigetti Ankaa-3 via AWS Braket, DynQ improves execution quality, recovers workloads lost under transient defects, and maintains stable output under concurrent batching. It reduces L1 error by up to 45.1% and improves output similarity by up to 19.1% on heterogeneous hardware, while eliminating observed baseline failures on real devices. These results position quantum virtualisation as a graph-driven systems problem and show that adaptive, quality-aware QVMs enable reliable multi-tenant quantum cloud services.