Traversability estimation is a key prerequisite for safe and efficient navigation of quadruped robots in unstructured environments. While previous research demonstrated the use of convolutional neural networks (CNNs) for classifying terrain heightmap patches into traversable and non-traversable categories, limitations in dataset size and shallow network architecture restricted model generalization. In this paper, we extend prior work by (i) expanding the simulated dataset from 12 to 60 diverse heightmaps and (ii) improving the CNN architecture by introducing deeper convolutional layers, batch normalization, dropout regularization, and the Adam optimizer. These modifications increased classification accuracy from 82% to 96%, significantly enhancing robustness across diverse terrain conditions. The proposed model is integrated into a traversability-aware path planning framework, enabling quadruped robots to select safer and smoother trajectories in complex terrains. Unlike handcrafted geometric features, the CNN-based method learns to extract relevant spatial patterns automatically. The increased dataset diversity not only improves classification accuracy but also ensures robustness across different terrain morphologies, including hills, slopes, rocky surfaces, and uneven patches. This work thus bridges the gap between limited simulation-based traversability studies and real-world deployment challenges.