Context. Non-radial oscillations, observed in thousands of red giants by the space missions CoRoT and Kepler, allow us to greatly improve our understanding of stellar structure and evolution in cool low-mass stars. The currently available Kepler light curves contain an outstanding amount of information, but a detailed analysis of the individual oscillation modes in the observed power spectra, also known as peak bagging, is computationally demanding and challenging to perform on a large number of targets. Aims: Our intent is to perform for the first time a peak bagging analysis on a sample of 19 low-mass low-luminosity red giants observed by Kepler for more than four years. This allows us to provide high-quality asteroseismic measurements that can be exploited for an intensive testing of the physics used in stellar structure models, stellar evolution, and pulsation codes, as well as for refining existing asteroseismic scaling relations in the red giant branch regime. Methods: For this purpose, powerful and sophisticated analysis tools are needed. We exploit the Bayesian code Diamonds, using an efficient nested sampling Monte Carlo algorithm, to perform both a fast fitting of the individual oscillation modes and a peak detection test based on the Bayesian evidence. Results: We find good agreement for the parameters estimated in the background fitting phase with those given in the literature. We extract and characterize a total of 1618 oscillation modes, providing the largest set of detailed asteroseismic mode measurements ever published. We report on the evidence of a change in regime observed in the relation between linewidths and effective temperatures of the stars occurring at the bottom of the red giant branch. We show the presence of a linewidth depression or plateau around νmax for all the red giants of the sample. Lastly, we show a good agreement between our measurements of maximum mode amplitudes and existing maximum amplitudes from global analyses provided in the literature, proving that amplitude scaling relations can be used as empirical tools to improve and simplify the future peak bagging analysis on a larger sample of evolved stars.