Hyperspectral LiDAR (HSL) enables the simultaneous acquisition of the surface geometry and spectral signatures of remote natural targets, making it valuable for various applications such as material probing, automated point cloud segmentation, and vegetation health monitoring. We present a first proof-of-concept study of a broadband dual-comb HSL system based on a 1 GHz dual-comb supercontinuum (SC). The SC spans from 820 to 1300 nm, generated via coherent spectral broadening of a free-running single-cavity dual-comb oscillator at 1053 nm in a single nonlinear photonic crystal fiber. The HSL system achieves a sub-µm ranging precision on a non-cooperative target at an update rate of 670 Hz. The shot-noise limited electronic dual-comb interferograms furthermore encode the spectral information of the target reflection across the SC bandwidth. This allows the capture of precise 3D point clouds with spectral signatures, unlocking new possibilities for spectrum-based material classification.