Underwater object classification by unmanned underwater vehicles (UUVs) is a critical task that is made difficult in shallow waters with concentrated particulate matter. Bistatic laser imaging is a current area of research that is more effective than traditional optical methods, but it requires separation of the laser receiver from the UUV-mounted laser emitter. This work explores the prospect of performing bistatic laser imaging with the receiver mounted to a quadrotor unmanned aerial vehicle (UAV). To facilitate the imaging application, estimation and guidance algorithms are developed to autonomously locate and track a UUV-mounted laser with an amphibious UAV. The UAV is equipped to carry a receiver payload in safe above-water flight and water landings. To represent the received laser measurements, laser intensity models are developed based on the distributions of the decollimated lasers used in the imaging application. The UAV autonomy is validated both in a reduced-order simulation environment and with the hardware testbed.