The Dosepix hybrid pixel detector was designed for dosimetry and radiation monitoring applications. It has three programmable modes of operation: photon counting mode, energy integration mode, and dosimetry mode. The dosimetry mode measures the energy of individual X-ray photons and automatically sorts events into pre-defined energy bins. The output is a histogram representing the measured X-ray energy spectrum, permitting a dose reconstruction that accounts for the attenuation of photons at each energy bin. This presents a potential radiation protection and dosimetry instrument in medical radiodiagnostic practices, including high flux systems such as computed tomography (CT). In this paper, we characterise the Dosepix chip by investigating the energy response and count rate capabilities when coupled to a 300μm silicon sensor under high fluxes of monochromatic synchrotron radiation. Under nominal settings, the Dosepix detector can detect photons down to 3.5keV, with an energy resolution of 16.5% FWHM for 8.5keV photons and 8% FWHM for 40keV photons. The chip can count up to 1.67Mcps/mm2 of 40keV photons whilst maintaining linear counting behaviour. This count rate range can be further increased by changing the programmable operating settings of the detector, making it suitable for a range of photon dosimetry applications.