Context. Large-scale cosmological simulations suggest that feedback from active galactic nuclei (AGN) plays a crucial role in galaxy evolution. More specifically, outflows are one of the mechanisms by which the accretion energy of the AGN is transferred to the interstellar medium (ISM), heating and driving out gas and impacting star formation (SF). Aims. The purpose of this study is to directly test this hypothesis utilising SDSS spectra of a well-defined sample of 48 low-redshift (z < 0.14) type 2 quasars (QSO2s). Methods. By exploiting these data, we were able to characterise the kinematics of the warm ionised gas by performing a non-parametric analysis of the [OIII]λ5007 emission line. We also constrained the properties of the young stellar populations (YSP; tysp < 100 Myr) of their host galaxies via spectral synthesis modelling. Results. These analyses revealed that 85% of the QSO2s display velocity dispersions in the warm ionised gas phase greater than that of the stellar component of their host galaxies, indicating the presence of AGN-driven outflows. We compared the gas kinematics with the intrinsic properties of the AGN and found that there is a positive correlation between gas velocity dispersion and 1.4 GHz radio luminosity – but not with the AGN bolometric luminosity or Eddington ratio. This either suggests that the radio luminosity is the key factor driving outflows or that the outflows themselves are shocking the ISM and producing synchrotron emission. We found that 98% of the sample host YSPs to varying degrees, with star formation rates (SFRs) of 0 ≤ SFR ≤ 92 M⊙ yr−1, averaged over 100 Myr. We compared the gas kinematics and outflow properties to the SFRs to establish possible correlations that could suggest that the presence of the outflowing gas could be impacting SF, but we found that no such correlation exists. This leads us to the conclusion that on the scales probed by the SDSS fibre (between 2 and 7 kpc diameters), AGN-driven outflows do not impact SF on the timescales probed in this study. However, we find a positive correlation between the light-weighted stellar ages of the QSO2s and the black hole mass, which might indicate that successive AGN episodes lead to the suppression of SF over the course of galaxy evolution.