We study the impact of the cosmological parameters uncertainties on the measurements of primordial non-Gaussianity through the large-scale non-Gaussian halo bias effect. While this is not expected to be an issue for the standard ΛCDM model, it may not be the case for more general models that modify the large-scale shape of the power spectrum. We consider the so-called local non-Gaussianity model, parametrized by the fNL non-Gaussianity parameter which is zero for a Gaussian case, and make forecasts on fNL from planned surveys, alone and combined with a Planck CMB prior. In particular, we consider EUCLID- and LSST-like surveys and forecast the correlations among fNL and the running of the spectral index αs, the dark energy equation of state w, the effective sound speed of dark energy perturbations c2s, the total mass of massive neutrinos Mν = ∑mν, and the number of extra relativistic degrees of freedom Nνrel. Neglecting CMB information on fNL and scales k > 0.03h/Mpc, we find that, if Nνrel is assumed to be known, the uncertainty on cosmological parameters increases the error on fNL by 10 to 30% depending on the survey. Thus the fNL constraint is remarkable robust to cosmological model uncertainties. On the other hand, if Nνrel is simultaneously constrained from the data, the fNL error increases by ~ 80%. Finally, future surveys which provide a large sample of galaxies or galaxy clusters over a volume comparable to the Hubble volume can measure primordial non-Gaussianity of the local form with a marginalized 1-σ error of the order ΔfNL ~ 2−5, after combination with CMB priors for the remaining cosmological parameters. These results are competitive with CMB bispectrum constraints achievable with an ideal CMB experiment.