3D Gaussian Splatting (3DGS) enables rapid differentiable rendering for 3D reconstruction and novel view synthesis, leading to its widespread commercial use. Consequently, copyright protection via watermarking has become critical. However, because 3DGS relies on millions of Gaussians, which require gigabytes of storage, efficient transfer and storage require compression. Existing 3DGS watermarking methods are vulnerable to quantization-based compression, often resulting in the loss of the embedded watermark. To address this challenge, we propose a novel watermarking method that ensures watermark robustness after model compression while maintaining high rendering quality. In detail, we incorporate a quantization distortion layer that simulates compression during training, preserving the watermark under quantization-based compression. Also, we propose a learnable watermark embedding feature that embeds the watermark into the anchor feature, ensuring structural consistency and seamless integration into the 3D scene. Furthermore, we present a frequency-aware anchor growing mechanism to enhance image quality in high-frequency regions by effectively identifying Guassians within these regions. Experimental results confirm that our method preserves the watermark and maintains superior image quality under high compression, validating it as a promising approach for a secure 3DGS model.