Recognizing the properties of the host galaxies of quasi-stellar objects (QSOs) is essential for understanding the suspected coevolution of central supermassive black holes (BHs) and their host galaxies. Low-luminosity type-1 QSOs (LLQSOs) are ideal targets because of their small cosmological distance, which allows for a detailed structural analysis. We selected a subsample of the Hamburg/ESO survey for bright UV-excess QSOs that contains only the 99 nearest QSOs with redshift z ≤ 0.06. From this LLQSO sample, we observed 20 galaxies and performed aperture photometry and bulge-disk-decomposition with BUDDA on near-infrared J-, H-, and K-band images to separate disk, bulge, bar, and nuclear component. From the photometric decomposition of these 20 objects and visual inspection of images of another 26, we find that ~50% of the hosts are disk galaxies and most of them (86%) are barred. Stellar masses, calculated from parametric models based on inactive galaxy colors, range from 2 × 109 M⊙ to 2 × 1011 M⊙ with an average mass of 7 × 1010 M⊙. Black hole masses measured from single-epoch spectroscopy range from 1 × 106 M⊙ to 5 × 108 M⊙ with a median mass of 3 × 107 M⊙. In comparison with higher-luminosity QSO samples, LLQSOs tend to have lower stellar and BH masses. Moreover, in the effective radius vs. mean surface-brightness projection of the fundamental plane, they lie in the transition area between luminous QSOs and normal galaxies. This can be seen as additional evidence that they populate a region intermediate between the local Seyfert population and luminous QSOs at higher redshift. This region has not been well studied so far. Eleven LLQSOs, for which we have reliable morphological decompositions and BH mass estimations, lie below the published BH mass vs. bulge luminosity relations for inactive galaxies. This can partially be explained if one assumes that the bulges of active galaxies contain much younger stellar populations than the bulges of inactive galaxies. Another possibility would be that their BHs are undermassive. This might indicate that the growth of the host spheroid precedes that of the BH.ASCII tables of the fit results are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://188.8.131.52) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/561/A140Figure 15 is available in electronic form at http://www.aanda.orgBased on observations with ESO-NTT, proposal no. 083.B-0739.