The time-dependent charging phenomenon of dust particles is timely studied in quantum plasmas with low frequency dust dynamical temporal scales referred to as dust acoustic waves. The quantum effects are incorporated through Fermi pressure, exchange-correlation potential as well as the Bohm potential. The quantum fluid model is employed in getting the dispersion relation pointing to the damping instability. The damping instability is analysed across the whole spectrum k, on varying ion-thermal temperature, electron number density and the dust radii. The applications of this work are pointed out in the laboratory and the astrophysical dense plasma systems.