Current quantum neural networks suffer from extreme sensitivity to both adversarial perturbations and hardware noise, creating a significant barrier to real-world deployment. Existing robustness techniques typically sacrifice clean accuracy or require prohibitive computational resources. We propose a hybrid quantum-classical Differentiable Quantum Architecture Search (DQAS) framework that addresses these limitations by jointly optimizing circuit structure and robustness through gradient-based methods. Our approach enhances traditional DQAS with a lightweight Classical Noise Layer applied before quantum processing, enabling simultaneous optimization of gate selection and noise parameters. This design preserves the quantum circuit's integrity while introducing trainable perturbations that enhance robustness without compromising standard performance. Experimental validation on MNIST, FashionMNIST, and CIFAR datasets shows consistent improvements in both clean and adversarial accuracy compared to existing quantum architecture search methods. Under various attack scenarios, including Fast Gradient Sign Method (FGSM), Projected Gradient Descent (PGD), Basic Iterative Method (BIM), and Momentum Iterative Method (MIM), and under realistic quantum noise conditions, our hybrid framework maintains superior performance. Testing on actual quantum hardware confirms the practical viability of discovered architectures. These results demonstrate that strategic classical preprocessing combined with differentiable quantum architecture optimization can significantly enhance quantum neural network robustness while maintaining computational efficiency.