A key obstacle to understanding the galaxy merger rate and its role in galaxy evolution is the difficulty in constraining the merger properties and time-scales from instantaneous snapshots of the real Universe. The most common way to identify galaxy mergers is by morphology, yet current theoretical calculations of the time-scales for galaxy disturbances are quite crude. We present a morphological analysis of a large suite of gadgetN-body/hydrodynamical equal-mass gas-rich disc galaxy mergers which have been processed through the Monte Carlo radiative transfer code sunrise. With the resulting images, we examine the dependence of quantitative morphology (G, M20, C, A) in the SDSS g band on merger stage, dust, viewing angle, orbital parameters, gas properties, supernova feedback and total mass. We find that mergers appear most disturbed in G−M20 and asymmetry at the first pass and at the final coalescence of their nuclei, but can have normal quantitative morphologies at other merger stages. The merger observability time-scales depend on the method used to identify the merger as well as the gas fraction, pericentric distance and relative orientation of the merging galaxies. Enhanced star formation peaks after and lasts significantly longer than strong morphological disturbances. Despite their massive bulges, the majority of merger remnants appear disc-like and dusty in g-band light because of the presence of a low-mass star-forming disc.