We determine the near-infrared Fundamental Plane (FP) for ∼104 early-type galaxies in the 6-degree Field Galaxy Survey (6dFGS). We fit the distribution of central velocity dispersion, near-infrared surface brightness and half-light radius with a 3D Gaussian model using a maximum-likelihood method. The model provides an excellent empirical fit to the observed FP distribution and the method proves robust and unbiased. Tests using simulations show that it gives superior results to regression techniques in the presence of significant and correlated uncertainties in all three parameters, censoring of the data by various selection effects and outliers in the data sample. For the 6dFGS J-band sample we find an FP with , similar to previous near-infrared determinations and consistent with the H- and K-band FPs once allowance is made for differences in mean colour. The overall scatter in Re about the FP is σr = 29 per cent, and is the quadrature sum of an 18 per cent scatter due to observational errors and a 23 per cent intrinsic scatter. Because of the Gaussian distribution of galaxies in FP space, σr is not the distance error, which we find to be σd = 23 per cent. Using group richness and local density as measures of environment, and morphologies based on visual classifications, we find that the FP slopes do not vary with environment or morphology. However, for fixed velocity dispersion and surface brightness, field galaxies are on average 5 per cent larger than galaxies in groups or higher density environments, and the bulges of early-type spirals are on average 10 per cent larger than ellipticals and lenticulars. The residuals about the FP show significant trends with environment, morphology and stellar population. The strongest trend is with age, and we speculate that age is the most important systematic source of offsets from the FP, and may drive the other trends through its correlations with environment, morphology and metallicity. These results will inform our use of the near-infrared FP in deriving relative distances and peculiar velocities for 6dFGS galaxies.