We investigate the nonequilibrium transport near a quantum phase transition in a generic and relatively simple model, the dissipative resonant level model, that has many applications for nanosystems. We formulate a rigorous mapping and apply a controlled frequency-dependent renormalization group approach to compute the nonequilibrium current in the presence of a finite bias voltage V and a finite temperature T. For V→0, we find that the conductance has its well-known equilibrium form, while it displays a distinct nonequilibrium profile at finite voltage.