Dumbbell-shaped fullerene dimers ${C}_{118}^{+}$ and ${C}_{119}^{+}$ have recently been observed in mass spectra resulting from collisions between clusters of C${}_{60}$ molecules and keV He${}^{2+}$ or Ar${}^{2+}$ ions [H. Zettergren et al., Phys. Rev. Lett. 110, 185501 (2013) and F. Seitz et al., J. Chem. Phys. 139, 034309 (2013)]. To unveil the formation mechanisms of these fullerene dimers, systematic molecular dynamics (MD) simulations based on the self-consistent charge density functional tight-binding method have been performed for C${}_{n}^{+}$ + C${}_{60}$ ($n=58,59,60$) collisions following prompt atom knockouts by the fast ions. The statistics from the MD simulations indicate a much higher reactivity of ${C}_{59}^{+}$ and ${C}_{58}^{+}$ fragments compared to that of ${C}_{60}^{+}$. It is found that the covalently bonded dumbbell-shaped fullerene dimers ${C}_{118}^{+}$ and ${C}_{119}^{+}$ can be formed at very low-collision energies within 1 ps and are stable enough to survive on the microsecond time scale of the experiment. The thermodynamic and kinetic stabilities, as well as the bonding features, have been investigated for the most stable dumbbell dimers ${C}_{118}^{+}$, ${C}_{119}^{+}$, and ${C}_{120}^{+}$.