We are exploring low-dose proton radiography and computed tomography (pCT) as techniques to improve the accuracy of proton treatment planning and to provide artifact-free images for verification and adaptive therapy at the time of treatment. Here we report on comprehensive beam test results with our prototype pCT head scanner. The detector system and data acquisition attain a sustained rate of more than a million protons individually measured per second, allowing a full CT scan to be completed in six minutes or less of beam time. In order to assess the performance of the scanner for proton radiography as well as computed tomography, we have performed numerous scans of phantoms at the Northwestern Medicine Chicago Proton Center including a custom phantom designed to assess the spatial resolution, a phantom to assess the measurement of relative stopping power, and a dosimetry phantom. Some images, performance, and dosimetry results from those phantom scans are presented together with a description of the instrument, the data acquisition system, and the calibration methods.