In recent years, a huge amount of mobility data has been collected from multiple sources, which has shown increasing utility in various domains such as transportation optimization, disease spread prediction and location-based services. However, trajectory data, a specific type of mobility data, raises substantial privacy concerns due to its high inference potential with respect to the personal information of users. To address this issue, we propose a new privacy-preserving trajectory data publication mechanism based on representation learning and differential privacy. Our approach is based on an effective and scalable trajectory-to-vector encoder that is based on a transformer neural architecture. First, we demonstrate that directly using such an encoder does not suffice to protect the original raw data, as the encoder can still expose information that may reflect individual characteristics of the underlying data, thus raising privacy concerns similar to those associated with directly sharing this data. More precisely, we show that an adversary that has access to the encoder can exploit it to conduct a successful Trajectory-User Linking (TUL) attack. Afterwards to address this issue, we introduce an efficient privacy-preserving trajectory-to-vector encoder, combining PATE (Private Aggregation of Teacher Ensemble) framework and Domain-Adaptive Pre-Training (DAPT), which provides a satisfying privacy-utility trade-off. In particular, the learned encoder can be employed as a building block for other mobility-related downstream tasks.