We present submillimetre continuum observations of a sample of some of the highest redshift quasars currently known, made with the SCUBA bolometer array on the JCMT. The median redshift of the sample is 5.3. Two z>5 objects are strong (6 sigma) detections, with S(850um)>10mJy. A firm (5 sigma) detection is obtained for the z=5.7 quasar SDSS J1044-0125; and SDSS J1306+0356, at z=6.0, is detected with a signal-to-noise approx. 4. For the remainder of the sample we have obtained sensitive (sigma=1.5mJy) upper limits. Submm spectral indices measured for two of the sources are consistent with thermal reradiation from dust, rather than from synchrotron emission. Sensitive 450um upper limits imply that the dust is cool,suggesting large dust masses only 1Gyr after the Big Bang.