Continuum emission from a total of 13 planetary nebulae (PN) has been detected at millimetre and submillimetre wavelengths, in all but one case for the first time. It was found that Type I and young, compact PN both have significant dust emission at 450 and 800-mu-m, while at 1100 and 2000-mu-m the free-free emission from the nebular gas dominates. More evolved PN do not usually show any cool dust excess above the free-free emission at 800-mu-m. We have also spatially resolved the cool dust in the neutral regions surrounding NGC 7027 and BD + 30-degrees 3639 for the first time. In NGC 7027 the 450-mu-m emission seems to correlate spatially with the optical extinction in front of the nebula and the CO emission. We model the IR submillimetre observations for NGC7027 and BD + 30-degrees 3639 using amorphous carbon dust; graphite not being able to provide enough submillimetre flux. In the ionized regions of these two young, compact nebulae we deduce that the dust-to-gas ratios are no higher than about 7 x 10(-4). This is similar to large older PN and, therefore, there is no evidence here that the dust content drops as PN evolve. The dust-to-gas ratio in the neutral region around NGC 7027 is about 1.5 x 10(-3), which means that dust is not significantly destroyed in the ionized region of the nebula.