Hyperspectral image super-resolution aims to enhance the spatial resolution of low-resolution hyperspectral images and is critical for applications such as remote sensing and precision agriculture. Existing deep learning methods have made significant progress, but they still struggle to capture complex long-range spatial-spectral dependencies and to fully exploit complementary information between spatial and spectral features. To address these challenges, we propose a dual-domain spatial-spectral aggregation Transformer (DSAT) for single-image hyperspectral super-resolution. Central to DSAT is dual-domain modeling and interactive aggregation in the spatial and spectral domains. Concretely, a bidirectional gated spatial-spectral aggregation (BGSA) module constructs cross-domain spatial self-attention and cross-domain spectral self-attention. The spatial branch injects global context into local-window self-attention to strengthen long-range spatial dependency modeling, while the spectral branch focuses on global relationships along the spectral dimension to accurately capture intrinsic correlations among bands. Moreover, an adaptive interaction module is embedded within BGSA to perform adaptive weighting and fusion of spatial-spectral features via spatial interaction and channel interaction, thereby exploiting complementarity between spatial and spectral information. Experiments on three benchmark datasets show that the proposed method outperforms other competitors in both objective metrics and visual quality.