We describe the design of a prototype preclinical PET/MR system capable of scanning small animals up to the size of a rabbit. The scanner uses highly sensitive and fast LSO/silicon-photomultiplier arrays as detector elements, direct digitization with a dedicated ASIC and integrated digital singles processing. Special measures are taken to improve the MR-compatibility of this design. Measurements of a prototype detector were performed inside 1.5 T and 3 T MRI-systems. Even under high gradient-slew-rates and RF-pulses disturbance energy- and coincidence timing-resolution of ~18% and 530 ps (FWHM) respectively have been measured. The presented work is part of the EU FP7 project HYPERImage, Grant Agreement N degrees 201651,.