In autodyne interferometry, the beating between the reference beam and the signal beam takes place inside the laser cavity and therefore the laser fulfills simultaneously the roles of emitter and detector of photons. In these conditions, the laser relaxation oscillations play a leading role, both in the laser quantum noise, which determines the signal-to-noise ratio (SNR), and also in the laser dynamics, which determines the response time of the interferometer. In the present study, we have experimentally analyzed the SNR and the response time of a laser optical feedback imaging (LOFI) interferometer based on a Nd(3+) microchip laser, with a relaxation frequency in the megahertz range. More precisely, we have compared the image quality obtained when the laser dynamics is free and when it is controlled by a stabilizing electronic feedback loop using a differentiator. From this study, we can conclude that when the laser time response is shorter (i.e., the LOFI gain is lower), the image quality can be better (i.e., the LOFI SNR can be higher) and that the use of an adapted electronic feedback loop allows high-speed LOFI with a shot-noise limited sensitivity. Despite the critical stability of the electronic feedback loop, the obtained experimental results are in good agreement with the theoretical predictions.