Human Activity Recognition (HAR) on memory-constrained edge devices demands heterogeneous, accurate, resource-adaptive architectures that are costly to design manually. Neural Architecture Search (NAS) provides an automated solution for model design, and its integration with quantization can further expose high-quality architectures under edge memory budgets. Recent NAS increasingly adopts LLM-based methods, including prompt-engineering and fine-tuning approaches. Prompt-engineering approaches suffer from 4-10 hours generation time, while fine-tuning approaches achieve minute-level generation but often sacrifice architecture quality due to the complexity of quantization. We propose QuaNAG, a Neural Architecture Generation (NAG) framework built on the insight that quantization is not an ordinary architecture attribute: it can change model feasibility, alter accuracy, and expand the feasible search space. QuaNAG therefore models quantization as branch-level search decisions and transfers quantization-aware search knowledge into an LLM through curriculum learning. Experiments on demanding HAR benchmarks over five baselines, including in-domain evaluations, out-of-domain evaluations, and on-device experiments, demonstrate that QuaNAG achieves 8.93% average accuracy improvement with several minutes generation time, satisfying all deployment requirements. Our code and model are available at https://github.com/pyq623/QuaNAG.