Quantum dot devices may be tuned to Kondo models which have non-interacting limits such as the Toulouse limit. At sufficiently low temperatures the Toulouse limit can be used to make predictions for charge transport in the devices driven away from equilibrium, e.g. with an ac bias. We investigate non-equilibrium transport in a resonant level model with a single lead which may be mapped onto the Toulouse limit of the one-channel Kondo model. The main results are expressions for the charge current that are exact in the tunnelling couplings, while remaining in the linear response regime of the time-dependent voltage bias. We also show how the line of enquiry directly extends to the tunnelling junction studied by A.~Schiller and S.~Hershfield in which a Kondo impurity interacts separately with two leads.