To study the nuclear (≲1 kpc) dust of nearby (z < 0.1) quasi-stellar objects (QSOs), we obtained new near-infrared (NIR) high angular resolution (~0.″3) photometry in the H and Ks bands for 13 QSOs with available mid-infrared (MIR) high angular resolution spectroscopy (~7.5-13.5 μm). We find that in most QSOs, the NIR emission is unresolved. We subtract the contribution from the accretion disk, which decreases from NIR (~35%) to MIR (~2.4%). We also estimate these percentages assuming a bluer accretion disk and find that the contribution in the MIR is nearly seven times larger. We find that the majority of objects (64%, 9/13) are better fitted by the disk+wind H17 model, while others can be fitted by the smooth F06 (14%, 2/13), clumpy N08 (7%, 1/13), clumpy H10 (7%, 1/13), and two-phase media S16 (7%, 1/13) models. However, if we assume the bluer accretion disk, the models fit only 2/13 objects. We measured two NIR-to-MIR spectral indexes, α NIR-MIR(1.6-8.7 μm) and α NIR-MIR(2.2-8.7 μm), and two MIR spectral indexes, α MIR(7.8-9.8 μm) and α MIR(9.8-11.7 μm), from models and observations. From observations, we find that the NIR-to-MIR spectral indexes are ~-1.1, and the MIR spectral indexes are ~-0.3. Comparing the synthetic and observed values, we find that none of the models simultaneously match the measured NIR-to-MIR and 7.8-9.8 μm slopes. However, we note that measuring α MIR(7.8-9.8 μm) on the starburst-subtracted Spitzer/IRS spectrum gives values of the slopes (~-2) that are similar to the synthetic values obtained from the models.