We consider a fixed-rate zero-delay source coding problem where a stationary vector-valued Gauss-Markov source is compressed subject to an average mean-squared error (MSE) dis-tortion constraint. We address the problem by considering the Gaussian nonanticipative rate distortion function (NRDF) which is a lower bound to the zero-delay Gaussian RDF. Then, we use its corresponding optimal 'test-channel' to characterize the stationary Gaus-sian NRDF and evaluate the corresponding information rates. We show that the Gaussian NRDF can be achieved by p-parallel fixed-rate scalar uniform quantizers of finite support with dithering signal up to a multiplicative distortion factor and a constant rate penalty. We demonstrate our framework with a numerical example.