In hadrontherapy in order to fully take advantage of the assets of the ion irradiation, the position of the Bragg peak has to be monitored accurately. Here, we investigate a monitoring method relying on the detection in real time of the prompt gamma emitted quasi instantaneously during the nuclear fragmentation processes. Our detection system combines a beam hodoscope and a double scattering Compton camera. The prompt-gamma emission points are reconstructed by intersecting the ion trajectories given by the hodoscope and the Compton cones reconstructed with the camera. We propose here to study in terms of point spread function and efficiency the theoretical feasibility of the emission points reconstruction with our set-up in the case of a photon point source in air. First we analyze the nature of all the interactions which are likely to produce an energy deposit in the three detectors of the camera. It is underlined that upper energy thresholds in both scatter detectors are required in order to select mainly Compton events (one Compton interaction in each scatter detector and one interaction in the absorber detector). Then, we study the influence of various parameters such as the photon energy and the inter-detector distances on the Compton camera response. These studies are carried out by means of Geant4 simulations. We use a source with a spectrum corresponding to the prompt-gamma spectrum emitted during the carbon ion irradiation of a water phantom. In the current configuration, the spatial resolution of the Compton camera is about 6 mm (Full Width at Half Maximum) and the detection efficiency 10^{-5}. Finally, provided the detection efficiency is increased, the clinical applicability of our system is considered.