Abstract: Mobile legged robots offer unique advantages for on-site construction, including the ability to traverse unstructured terrain, climb stairs, and operate independently between spatially separated work zones. This paper presents a proof-of-concept system for autonomous brick stacking using a Boston Dynamics Spot quadrupedal robot equipped with a manipulator arm. The system operates between a supply area and an assembly area, using AprilTag fiducials for localization and autowalk missions for navigation. Target brick positions and orientations are specified in CAD software and exported directly for robotic execution. We evaluate placement accuracy through ten repeated assemblies of a curved four-layer wall comprising 14 wooden bricks. Results show mean translation errors below 10 mm and mean yaw errors below 1.5 degrees, while the overall RMSE across all runs is 27.72 mm (translation) and 2.06 degrees (rotation). The system was also tested outdoors with stairs between the two areas. The workflow is modular and easily extendable to different wall geometries.