We demonstrate the applicability of propagation-based X-ray phase-contrast imaging at a laser-assisted compact light source with known phantoms and the lungs and airways of a mouse. The Munich Compact Light Source provides a quasi-monochromatic beam with partial spatial coherence, and high flux relative to other non-synchrotron sources (up to 1010 ph/s). In our study we observe significant edge-enhancement and quantitative phase-retrieval is successfully performed on the known phantom. Furthermore the images of a small animal show the potential for live bio-imaging research studies that capture biological function using short exposures.