Distributed Source Coding (DSC) has been widely studied in applications such as video coding and distributed sensor networks. However, DSC has not been widely explored for low delay and low bit rate applications such as quantization of speech Line Spectral Frequencies (LSFs). This is due to the difficulty of modeling and analyzing the effects of imperfect side information resulting from the previous packet losses, quantization noise and decoding errors. In this paper, we present methods for modeling, analyzing and designing Wyner-Ziv(WZ) quantizers for jointly Gaussian vector data with imperfect side information. In particular, we show the decomposition of the quantizer design problem for the vector data into independent scalar design subproblems. Then we demonstrate the analytical techniques to compute the optimum step size and bit allocation for each scalar dimension to minimize the decoder expected Mean Squared Error(MSE). The simulation results verify the analytical results obtained in this paper.