Dwarf ellipticals are the most common galaxy type in cluster environments; however, the challenges associated with their observation mean that their formation mechanisms are still poorly understood. To address this, we present deep integral field observations of a sample of 31 low-mass (107.5 < M⋆ < 109.5 M☉) early-type galaxies in the Fornax cluster with the SAMI instrument. For 21 galaxies, our observations are sufficiently deep to construct spatially resolved maps of the stellar velocity and velocity dispersion - for the remaining galaxies, we extract global velocities and dispersions from aperture spectra only. From the kinematic maps, we measure the specific stellar angular momentum λR of the lowest mass dE galaxies to date. Combining our observations with early-type galaxy data from the literature spanning a large range in stellar mass, we find that λR decreases towards lower stellar mass, with a corresponding increase in the proportion of slowly rotating galaxies in this regime. The decrease of λR with mass in our sample dE galaxies is consistent with a similar trend seen in somewhat more massive spiral galaxies from the CALIFA survey. This suggests that the degree of dynamical heating required to produce dEs from low-mass starforming progenitors may be relatively modest and consistent with a broad range of formation mechanisms.