We present a functional renormalization group approach to the zero bias transport properties of a quantum dot with two different orbitals and in the presence of Hunds coupling. Tuning the energy separation of the orbital states, the quantum dot can be driven through a singlet-triplet transition. Our approach, based on the approach by Karrasch etal (2006 Phys. Rev. B 73 235337), which we apply to spin-dependent interactions, recovers the key characteristics of the quantum dot transport properties with very little numerical effort. We present results on the conductance in the vicinity of the transition and compare our results both with previous numerical renormalization group results and with predictions of the perturbative renormalization group.