Laser-accelerated proton beams exhibit remarkably different beam characteristics as compared to conventionally accelerated ion beams. About 105 to 107 particles per MeV and msr are accelerated quasi-instantaneously within about 1 ps. The resulting energy spectrum typically shows an exponentially decaying distribution. Our planned approach to determine the energy spectrum of the particles generated in each pulse is to exploit the time-of-flight (TOF) difference of protons with different kinetic energies at 1 m distance from the laser-target interaction. This requires fast and sensitive detectors. We therefore tested two prototype silicon detectors, developed at the Centre for Medical Radiation Physics at the University of Wollongong with a current amplifier, regarding their suitability for TOF-spectrometry in terms of sensitivity and timing properties. For the latter, we illuminated the detectors with short laser pulses, measured the signal current and compared it to the signal of a fast photodiode. The comparison revealed that the timing properties of both prototypes are not yet sufficient for our purpose. In contrast, our results regarding the detectors' sensitivity are promising. The lowest detectable proton flux at 10 MeV was found to be 25 protons per ns on the detector. With this sensitivity and with a smaller pixelation of the detectors, the timing properties can be improved for new prototypes, making them potential candidates for TOF-spectrometry of laser-accelerated particle beams.