Context. Disc-halo decompositions z = 1 − 2 star-forming galaxies (SFGs) at z > 1 are often limited to massive galaxies (M > 10 10 M ) and rely on either deep Integral Field Spectroscopy data or stacking analyses. Aims. We present a study of the dark-matter (DM) content of 9 z ≈ 1 SFGs selected among the brightest [O ii] emitters in the deepest Multi-Unit Spectrograph Explorer (MUSE) field to date, namely the 140hr MUSE Extremely Deep Field. These SFGs have low stellar masses, ranging from 10 8.5 to 10 10.5 M . Methods. We analyze the kinematics with a 3D modeling approach, which allows us to measure individual rotation curves to ≈ 3 times the half-light radius R e . We perform disk-halo decompositions on their [O ii] emission line with a 3D parametric model, which does not require external information on the inclination, concentration nor on the disk stellar mass. The disk-halo decomposition includes a stellar, DM, gas and occasionally a bulge component. The DM component primarily uses the generalized α, β, γ profile from Di Cintio et al., or a Navarro-Frenk-White (NFW) profile.Results. The disk stellar masses M obtained from the [O ii] disk-halo decomposition agree with the values inferred from the spectral energy distributions. While the rotation curves show diverse shapes, ranging from rising to declining at large radii, the DM fractions within the half-light radius f DM (< R e ) are found to be 60% to 95%, extending to lower masses (densities) the results of Genzel et al., who found low DM fractions in SFGs with M > 10 10 M . The DM halos show constant surface densities of ∼ 100 M pc −2 . For isolated galaxies, half of the sample shows a strong preference for cored over cuspy DM profiles. The presence of DM cores appears to be related to galaxies with low stellar-to-halo mass ratio, log M /M vir ≈ −2.5. In addition, the cuspiness of the DM profiles is found to be a strong function of the recent star-formation activity. Conclusions. We measured the properties of DM halos on scales from 1 to 15 kpc, put constraints on the z > 0 c vir − M vir scaling relation, and unveiled the cored nature of DM halos in some z 1 SFGs. These results support feedback induced core formation in the Cold Dark Matter context.