A simple quantum-defect model gives analytic expressions for the complex scattering length and threshold collision rates of ultracold molecules. If the probability of reaction in the short-range part of the collision is high, the model gives universal rate constants for s- and p-wave collisions that are independent of short-range dynamics. This model explains the magnitudes of the recently measured rate constants for collisions of two ultracold (40)K(87)Rb molecules, or an ultracold (40)K atom with the (40)K(87)Rb molecule [S. Ospelkaus et al., Science 327, 853 (2010)].