We introduce Bayesian QuickNAT for the automated quality control of whole-brain segmentation on MRI T1 scans. Next to the Bayesian fully convolutional neural network, we also present inherent measures of segmentation uncertainty that allow for quality control per brain structure. For estimating model uncertainty, we follow a Bayesian approach, wherein, Monte Carlo (MC) samples from the posterior distribution are generated by keeping the dropout layers active at test time. Entropy over the MC samples provides a voxel-wise model uncertainty map, whereas expectation over the MC predictions provides the final segmentation. Next to voxel-wise uncertainty, we introduce four metrics to quantify structure-wise uncertainty in segmentation for quality control. We report experiments on four out-of-sample datasets comprising of diverse age range, pathology and imaging artifacts. The proposed structure-wise uncertainty metrics are highly correlated with the Dice score estimated with manual annotation and therefore present an inherent measure of segmentation quality. In particular, the intersection over union over all the MC samples is a suitable proxy for the Dice score. In addition to quality control at scan-level, we propose to incorporate the structure-wise uncertainty as a measure of confidence to do reliable group analysis on large data repositories. We envisage that the introduced uncertainty metrics would help assess the fidelity of automated deep learning based segmentation methods for large-scale population studies, as they enable automated quality control and group analyses in processing large data repositories.