Daunomycin (DN) is a well-known chemotherapy drug frequently used in treating acute myeloid and lymphoblastic leukemia. It needs to be delivered to the therapeutic target by a delivering agent that beats the blood-brain barrier. DN is known to be specifically located at the membrane surface and scantly to the bilayer. Penetration of DN into the membrane bilayer depends on the molecular packing of the lipid. It does not travel promptly to the interior of the cells and needs a carrier to serve the purpose. Here, we have demonstrated, by fluorescence lifetime imaging spectroscopy (FLIM) and resonance energy transfer (RET) phenomenon, that ultrasmall graphene quantum dots (GQDs) can be internalized into the aqueous pool of giant unilamellar vesicles (GUVs) made from dipalmitoylphosphatidylcholine (DPPC) lipids, which, in turn, help in fast translocation of DN through the membrane without any delivery vehicle.