We present a detailed analysis of all the known hot DQ white dwarfs in the Fourth Data Release of the Sloan Digital Sky Survey (SDSS) recently found to have carbon-dominated atmospheres. Our spectroscopic and photometric analysis reveals that these objects all have effective temperatures between ~18,000 and 24,000 K. The surface composition is found to be completely dominated by carbon, as revealed by the absence of Hβ and He I λ4471 lines (or a determination of trace amounts in a few cases). We find that the surface gravity of all objects but one seems to be "normal" and around log g = 8.0, while one is likely near log g = 9.0. The presence of a weak magnetic field is directly detected by spectropolarimetry in one object and is suspected in two others. We propose that these strange stars could be cooled-down versions of the weird PG 1159 star H1504+65 and form a new family of hydrogen- and helium-deficient objects following the post-AGB phase. Finally, we present the results of full nonadiabatic calculations dedicated specifically to each of the hot DQs that show that only SDSS J142625.70+575218.4 is expected to exhibit luminosity variations. This result is in excellent agreement with recent observations by Montgomery et al., who find that J142625.70+575218.4 is the only pulsator among six hot DQ white dwarfs surveyed in 2008 February.