A critical aspect of safe and efficient motion planning for autonomous vehicles (AVs) is to handle the complex and uncertain behavior of surrounding human-driven vehicles (HDVs). Despite intensive research on driver behavior prediction, existing approaches typically overlook the interactions between AVs and HDVs assuming that HDV trajectories are not affected by AV actions. To address this gap, we present a transformer-transfer learning-based interaction-aware trajectory predictor for safe motion planning of autonomous driving, focusing on a vehicle-to-vehicle (V2V) interaction scenario consisting of an AV and an HDV. Specifically, we construct a transformer-based interaction-aware trajectory predictor using widely available datasets of HDV trajectory data and further transfer the learned predictor using a small set of AV-HDV interaction data. Then, to better incorporate the proposed trajectory predictor into the motion planning module of AVs, we introduce an uncertainty quantification method to characterize the errors of the predictor, which are integrated into the path-planning process. Our experimental results demonstrate the value of explicitly considering interactions and handling uncertainties.