We modify the chemo-dynamical code GEAR to simulate the impact of self-interacting dark matter (SIDM) on the observable quantities of 19 low-mass dwarf galaxies with a variety star-forming properties. We employ a relatively high, velocity independent cross-section of sigma/m =10cm(2) g(-1) and extract, in addition to integrated quantities, the total mass density profile, the luminosity profile, the line-of-sight velocities, the chemical abundance, and the star formation history. We find that despite the creation of large cores at the centre of the dark matter haloes, the impact of SIDM on the observable quantities of quenched galaxies is indiscernible, dominated mostly by the stochastic build up of the stellar matter. As such we conclude that it is impossible to make global statements on the density profile of dwarf galaxies from single or small samples. Although based mostly on quenched galaxies, this finding supports other recent work putting into question the reliability of inferred cored density profiles that are derived from observed line-of-sight velocities.