Dwarf irregular galaxies, due to their lower masses, relative isolation, and high-quality data availability, are ideal laboratories to test various models of dark matter. In particular, the existence, morphology and formation of central cores in dwarf galaxies has been a contentious issue in the literature in light of apparent tensions with the standard cosmological model. By analyzing a robust sample of rotation curves of these objects and comparing them with simulations, we explore the adequacy of various models of interest to explain these observations, including supernovae-driven baryonic feedback models, fuzzy dark matter, and self-interacting dark matter. From this, one can infer predicted parameters of models and establish statistical correlations in core morphology parameters which are not trivially satisfied by the theory, including cases where tensions may arise. It is then possible to potentially favor or exclude these models based on the analysis performed.