We present a catalogue of prestellar and starless cores within the Corona Australis molecular cloud using photometric data from the Herschel Space Observatory. At a distance of d~130pc, Corona Australis is one of the closest star-forming regions. Herschel has taken multi-wavelength data of Corona Australis with both the Spectral and Photometric Imaging Receiver (SPIRE; Griffin et al. 2010A&A...518L...3G) and the Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010A&A...518L...2P) photometric cameras in a parallel mode with wavelengths in the range 70um to 500um. A complete sample of starless and prestellar cores and embedded protostars is identified. Other results from the Herschel Gould Belt Survey have shown spatial correlation between the distribution of dense cores and the filamentary structure within the molecular clouds. We go further and show correlations between the properties of these cores and their spatial distribution within the clouds, with a particular focus on the mass distribution of the dense cores with respect to their filamentary proximity. We find that only lower-mass starless cores form away from filaments, while all of the higher-mass prestellar cores form in close proximity to or directly on the filamentary structure. This result supports the paradigm that prestellar cores mostly form on filaments. We analyse the mass distribution across the molecular cloud, finding evidence that the region around the Coronet appears to be at a more dynamically advanced evolutionary stage in comparison to the rest of the clumps within the cloud.