Ghost imaging reconstructs spatial information from a single-pixel bucket detector by correlating structured illumination patterns with scalar intensity measurements. While deep learning approaches have achieved promising results on static scenes, two critical limitations remain unaddressed: existing architectures fail to exploit temporal coherence across frames, leaving dynamic ghost imaging largely unsolved, and they assume additive Gaussian noise models that do not reflect the true Poissonian statistics of real single-photon hardware. We present DynGhost (Dynamic Ghost Imaging Transformer), a transformer architecture that addresses both limitations through alternating spatial and temporal attention blocks. Our quantum-aware training framework, based on physically accurate detector simulations (SNSPDs, SPADs, SiPMs) and Anscombe variance-stabilizing normalization, resolves the distribution shift that causes classical models to fail under realistic hardware constraints. Experiments across multiple benchmarks demonstrate that DynGhost outperforms both traditional reconstruction methods and existing deep learning architectures, with particular gains in dynamic and photon-starved settings.