Graph Domain Adaptation (GDA) facilitates knowledge transfer from labeled source graphs to unlabeled target graphs by learning domain-invariant representations, which is essential in applications such as molecular property prediction and social network analysis. However, most existing GDA methods rely on the assumption of clean source labels, which rarely holds in real-world scenarios where annotation noise is pervasive. This label noise severely impairs feature alignment and degrades adaptation performance under domain shifts. To address this challenge, we propose Nested Graph Pseudo-Label Refinement (NeGPR), a novel framework tailored for graph-level domain adaptation with noisy labels. NeGPR first pretrains dual branches, i.e., semantic and topology branches, by enforcing neighborhood consistency in the feature space, thereby reducing the influence of noisy supervision. To bridge domain gaps, NeGPR employs a nested refinement mechanism in which one branch selects high-confidence target samples to guide the adaptation of the other, enabling progressive cross-domain learning. Furthermore, since pseudo-labels may still contain noise and the pre-trained branches are already overfitted to the noisy labels in the source domain, NeGPR incorporates a noise-aware regularization strategy. This regularization is theoretically proven to mitigate the adverse effects of pseudo-label noise, even under the presence of source overfitting, thus enhancing the robustness of the adaptation process. Extensive experiments on benchmark datasets demonstrate that NeGPR consistently outperforms state-of-the-art methods under severe label noise.