The resonant-level model is a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model [1-4]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization group approach [5] is applied to compute the non-equilibrium current in the presence of a finite bias voltage V. In the linear response regime V ->0, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the non-equilibrium transport near the quantum phase transition. We furthermore provide new signatures of the transition in the finite-frequency current noise and AC conductance via the recently developed Functional Renormalization Group (FRG) approach. Our work on dissipative resonant level has direct relevance to the experiments in a quantum dot coupled to resistive environment done at Duke, namely H. Mebrahtu et al., Nature 488, 61, (2012).