Context : The youngest Galactic supernova remnant G1.9+0.3 is an interesting target for next generation gamma-ray observatories . So far , the remnant is only detected in the radio and the X-ray bands , but its young age of \approx 100 yrs and inferred shock speed of \approx 14 , 000 km/s could make it an efficient particle accelerator . Aims : We aim to model the observed radio and X-ray spectra together with the morphology of the remnant . At the same time , we aim to estimate the gamma-ray flux from the source and evaluated the prospects of its detection with future gamma-ray experiments . Methods : We performed spherical symmetric 1-D simulations with the RATPaC code , in which we simultaneously solve the transport equation for cosmic rays , the transport equation for magnetic turbulence , and the hydro-dynamical equations for the gas flow . Separately computed distributions of the particles accelerated at the forward and the reverse shock are then used to calculate the spectra of synchrotron , inverse Compton , and pion-decay radiation from the source . Results : The emission from G1.9+0.3 can be self-consistently explained within the test-particle limit . We find that the X-ray flux is dominated by emission from the forward shock while most of the radio emission originates near the reverse shock , which makes G1.9+0.3 the first remnant with non-thermal radiation detected from the reverse shock . The flux of very-high-energy gamma-ray emission from G1.9+0.3 is expected to be close to the sensitivity threshold of the Cherenkov Telescope Array , CTA . The limited time available to grow large-scale turbulence limits the maximum energy of particles to values below 100 TeV , hence G1.9+0.3 is not a PeVatron . Conclusions :