We present sensitive near–infrared VLT ISAAC spectroscopic observations of the z = 6.08 quasar SDSS J030331.40 - 001912.9 . This QSO is more than a magnitude fainter than other QSOs at z \sim 6 for which NIR spectroscopy has been obtained to date and is therefore presumably more representative of the QSO population at the end of Cosmic Reionization . Combining rest–frame UV continuum luminosity with the width measurements of the Mg ii and C iv lines , we derive a black hole mass of 2 ^ { +1.0 } _ { -0.5 } \times 10 ^ { 8 } M _ { \odot } , the lowest mass observed for z \sim 6 QSOs to date , and derive an Eddington ratio of 1.6 ^ { +0.4 } _ { -0.6 } , amongst the highest value derived for QSOs at any redshift . The Spitzer 24 \mu m non–detection of this QSO does not leave space for a significant hot dust component in its optical/near–infrared SED , in common with one other faint QSO at z = 6 , but in contrast to more than twenty more z = 6 QSOs and all known lower redshift QSOs with sufficiently deep multi-wavelength photometry . We conclude that we have found evidence for differences in the intrinsic properties of at least one z \sim 6 QSO as compared to the lower–redshift population .