Turbojet-powered VTOL UAVs have garnered increased attention in heavy-load transport and emergency services, due to their superior power density and thrust-to-weight ratio compared to existing electronic propulsion systems. The main challenge with jet-powered UAVs lies in the complexity of thrust vectoring mechanical systems, which aim to mitigate the slow dynamics of the turbojet. In this letter, we introduce a novel turbojet-powered UAV platform named Hex-Jet. Our concept integrates thrust vectoring and differential thrust for comprehensive attitude control. This approach notably simplifies the thrust vectoring mechanism. We utilize a predictor-based time delay control method based on the frequency domain model in our Hex-Jet controller design to mitigate the delay in roll attitude control caused by turbojet dynamics. Our comparative studies provide valuable insights for the UAV community, and flight tests on the scaled prototype demonstrate the successful implementation and verification of the proposed predictor-based time delay control technique.