Widely linear model has recently been used for signal processing applications due to its ability to achieve better performance than conventional linear filtering for non-circular complex random variables (CRVs) and improper quaternion random variables (QRVs). In this paper, we study the time-domain widely linear quaternion model based minimum variance distortionless response beamformer (WL-QMVDR) for a single acoustic vector sensor (AVS) and analyze its performance in general through the use of beampatterns. We verify by simulation results that the estimated output of the WL-QMVDR is identical to the conventional linear model based MVDR beamformer when applied to an AVS in the non-reverberant and ideal sensor response scenario.