An integrated dosimetry and cell irradiation system (IDOCIS) with laser-accelerated proton beams was developed, characterized, calibrated and successfully used for systematic in vitro experiments. Due to the broad exponentially shaped energy spectrum, the low-energy range of the protons (<20 MeV) and the high pulse dose, the absolute dosimetry for this beam quality is challenging. Therefore, a dedicated Faraday cup is used as an energy and dose rate independent absolute dosimeter that has been calibrated consistently with three independent methods. A transmission ionization chamber providing online relative dose information is cross-calibrated against the Faraday cup. Providing both online and absolute dose information, the IDOCIS allows for quantitative dosimetric and radiobiological studies at current low-energy laser-accelerated proton beams. Finally, first dosimetric characterizations of a laser-accelerated proton beam with the IDOCIS are presented.