Stereo depth estimation is a fundamental component in augmented reality (AR) applications. Although AR applications require very low latency for their real-time applications, traditional depth estimation models often rely on time-consuming preprocessing steps such as rectification to achieve high accuracy. Also, non standard ML operator based algorithms such as cost volume also require significant latency, which is aggravated on compute resource-constrained mobile platforms. Therefore, we develop hardware-friendly alternatives to the costly cost volume and preprocessing and design two new models based on them, MultiHeadDepth and HomoDepth. Our approaches for cost volume is replacing it with a new group-pointwise convolution-based operator and approximation of consine similarity based on layernorm and dot product. For online stereo rectification (preprocessing), we introduce homograhy matrix prediction network with a rectification positional encoding (RPE), which delivers both low latency and robustness to unrectified images, which eliminates the needs for preprocessing. Our MultiHeadDepth, which includes optimized cost volume, provides 11.8-30.3% improvements in accuracy and 22.9-25.2% reduction in latency compared to a state-of-the-art depth estimation model for AR glasses from industry. Our HomoDepth, which includes optimized preprocessing (Homograhpy + RPE) upon MultiHeadDepth, can process unrectified images and reduce the end-to-end latency by 44.5%. We adopt a multi-task learning framework to handle misaligned stereo inputs on HomoDepth, which reduces theAbsRel error by 10.0-24.3%. The results demonstrate the efficacy of our approaches in achieving both high model performance with low latency, which makes a step forward toward practical depth estimation on future AR devices.