Quantum federated learning (QFL) emerges as a powerful technique that combines quantum computing with federated learning to efficiently process complex data across distributed quantum devices while ensuring data privacy in quantum networks. Despite recent research efforts, existing QFL frameworks struggle to achieve optimal model training performance primarily due to inherent heterogeneity in terms of (i) quantum noise where current quantum devices are subject to varying levels of noise due to varying device quality and susceptibility to quantum decoherence, and (ii) heterogeneous data distributions where data across participating quantum devices are naturally non-independent and identically distributed (non-IID). To address these challenges, we propose a novel integrated sporadic-personalized approach called SPQFL that simultaneously handles quantum noise and data heterogeneity in a single QFL framework. It is featured in two key aspects: (i) for quantum noise heterogeneity, we introduce a notion of sporadic learning to tackle quantum noise heterogeneity across quantum devices, and (ii) for quantum data heterogeneity, we implement personalized learning through model regularization to mitigate overfitting during local training on non-IID quantum data distributions, thereby enhancing the convergence of the global model. Moreover, we conduct a rigorous convergence analysis for the proposed SPQFL framework, with both sporadic and personalized learning considerations. Theoretical findings reveal that the upper bound of the SPQFL algorithm is strongly influenced by both the number of quantum devices and the number of quantum noise measurements. Extensive simulation results in real-world datasets also illustrate that the proposed SPQFL approach yields significant improvements in terms of training performance and convergence stability compared to the state-of-the-art methods.