Recurrent neural network based solutions are increasingly being used in the analysis of longitudinal Electronic Health Record data. However, most works focus on prediction accuracy and neglect prediction uncertainty. We propose Deep Kernel Accelerated Failure Time models for the time-to-event prediction task, enabling uncertainty-awareness of the prediction by a pipeline of a recurrent neural network and a sparse Gaussian Process. Furthermore, a deep metric learning based pre-training step is adapted to enhance the proposed model. Our model shows better point estimate performance than recurrent neural network based baselines in experiments on two real-world datasets. More importantly, the predictive variance from our model can be used to quantify the uncertainty estimates of the time-to-event prediction: Our model delivers better performance when it is more confident in its prediction. Compared to related methods, such as Monte Carlo Dropout, our model offers better uncertainty estimates by leveraging an analytical solution and is more computationally efficient.