The nd and pd breakup differential cross sections for the nucleon laboratory energies E_N ≤ 65 MeV are examined using the energy-independent quark-model nucleon-nucleon interaction fss2. The Coulomb effect is incorporated by the sharp cut-off Coulomb force, acting between quarks, without the phase-shift renormalization for the breakup amplitudes. Our model yields the results very similar to the meson-exchange potentials, including disagreement with experimental data for some specific kinematical configurations. This includes the notorious space star anomaly of the nd and pd scattering at E_N = 13 MeV. The shape of the pp final-state interaction peak in E_d = 130 MeV dp scattering data from KVI is not correctly reproduced, probably because the half off-shell behavior of the two-proton t-matrix is not appropriate in our Coulomb treatment.