In the present work, several efforts have been made theoretically to achieve an excellent non-toxic fluorescent graphene quantum dot (GQD) in the near-infrared region for the application of bio-imaging and sensing. Although the QY of GQDs is a maximum of 98.5% in the visible region, it is still very low, and it is as low as 7% in NIR. Sulfur and its group elements have been used for doping because they are pretty cheap and nontoxic and hence suitable for this application. The surface-doped position is considered for studying their effect on the energy band gap, absorption and fluorescence properties. The HOMO and LUMO isosurfaces have been analyzed in order to comprehend the nature of the dominant transition taking place in absorption spectra. Additionally, the quantitative indices, transition density matrix contour maps, and charge difference density have all been examined in order to determine whether this particular transition is locally excited or involves charge transfer. Following this, the QY of each GQD has been determined by considering the fluorescence spectra. The wavelength of fluorescence of doped GQDs is found to be in the region of 800-1400 nm, i.e. in NIR, which is strongly desirable for bio-imaging and bio-sensing applications. With a fluorescence of ~ 850 nm, sulfur-doped GQDs (S-GQD: C52S2H18) have the greatest QY, 26%, which is larger than the 7% achieved earlier in NIR and such a high QY in NIR is being reported for the first time.