The focus of dark matter searches to date has been on Weakly Interacting Massive Particles (WIMPs) in the GeV/c2-TeV/c2 mass range. The direct, indirect and collider searches in this mass range have been extensive but ultimately unsuccessful, providing a strong motivation for widening the search outside this range. Here we describe a new concept for a dark matter experiment, employing superfluid 3He as a detector for dark matter that is close to the mass of the proton, of order 1 GeV/c2. The QUEST-DMC detector concept is based on quasiparticle detection in a bolometer cell by a nanomechanical resonator. In this paper we develop the energy measurement methodology and detector response model, simulate candidate dark matter signals and expected background interactions, and calculate the sensitivity of such a detector. We project that such a detector can reach sub-eV nuclear recoil energy threshold, opening up new windows on the parameter space of both spin-dependent and spin-independent interactions of light dark matter candidates.