While fewer in number than the dominant rotation-powered radio pulsar population, peculiar classes of isolated neutron stars (INSs) -- which include magnetars, the ROSAT-discovered "Magnificent Seven" (M7), rotating radio transients (RRATs), and central compact objects in supernova remnants (CCOs) -- represent a key element in understanding the neutron star phenomenology. We report the results of an observational campaign to study the properties of the source 2XMM J104608.7-594306. Its evolutionary state is investigated by means of deep dedicated observations obtained with XMM-Newton, the ESO Very Large Telescope, as well as publicly available gamma-ray data from the Fermi and AGILE missions. The observations confirm previous expectations and reveal a unique type of object. The source, which is likely within the Carina Nebula, has a soft spectrum with absorption features and no magnetospheric emission. The optical counterpart is fainter than V=27 and no gamma-ray emission is significantly detected. Very interestingly, while these characteristics are remarkably similar to those of the M7 or the only RRAT so far detected in X-rays, which all have spin periods of a few seconds, we found intriguing evidence of very rapid rotation, P=18.6 ms. We interpret these new results in the light of the observed properties of the currently known neutron star population, in particular those of standard rotation-powered pulsars, recycled objects, and CCOs. We find that none of these scenarios can satisfactorily explain the collective properties of 2XMM J104608.7-594306, although it may be related to the still poorly known class of Galactic anti-magnetars. Future XMM-Newton data, granted for the next cycle of observations (AO11), will help us to improve our current observational interpretation of the source, enabling us to significantly constrain the rate of pulsar spin down.