This paper presents an underwater laser scanning system and GNSS based trajectory estimation system for scanning from a surface vessle in shallow water. The system has an above-the-water and an underwater component. Above-the-water two low-cost multiband GNSS receivers with an antenna baseline of one meter are used for RTK positioning with heading. The full 6-DOF is estimated by fusing the satellite navigation data with a MEMS-based INS. The 3D data is captured in water using a structured light scanner consisting of a low-light underwater camera and a green cross line laser projector. We describe the development of the system and employed hardware components. We show results of scanning a large test object in a water tank acquired by from a tripod with a motorized yaw axis. Additionally, we demonstrate first results of mobile mapping from a floating platform. We evaluate the performance of the system by measuring the 6-DOF trajectory with an external optical tracking system. Additionally, we assess the quality of the created point cloud using reference objects placed in the scene.