This paper aims at addressing the problem of global adaptive stabilisation by output feedback for a class of nonlinear systems, in which both the input and output are logarithmically quantised. The nonlinear functions of the systems are not necessary to be completely known and contain time-varying parameters that belong to an unknown bounded set. Based on dynamic high-gain technique, a linear-like quantised controller computed from quantised output is constructed and a guideline is derived to select the parameters of the quantisers. It is proved that, with the proposed scheme, all the states of the system can be globally steered to the origin while keeping the other signals of the closed-loop system bounded.