Despite its utility in exploring possible spatial variations in the stellar populations in galaxies, infrared surface photometry of low-luminosity dwarf elliptical (dE) galaxies is generally lacking, due to the technical difficulties in observing low surface brightness objects against the bright infrared sky. Here we attempt to remedy this shortfall to some extent by presenting K-band photometry at arcsecond resolution, including radial profiles, 1D and 2D model fits and the quantification of nuclear components, for a small sample of dE galaxies, with absolute magnitudes MB≃-15 to -13, in the Fornax Cluster. In the second part of the paper, we explore the comparison of these data with corresponding optical observations and attempt to interpret this in terms of stellar population models and their radial trends. A significant range of global optical-infrared colours is present in our sample, but radial colour gradients in the galaxies are usually small. However, while the nuclear regions tend to be bluer in optical colours, they are systematically redder than the surrounding galaxy in (R-K). The stellar population modelling suggests that these colour differences are probably an effect of both higher metallicity and younger age in the nuclei. Excluding the nuclear regions, the global colour profiles typically change in the same direction, again indicating older, more metal-poor stellar populations in the outskirts of the galaxies.