[en] We use quantum Monte Carlo methods to compute the density profile, the nonclassical moment of inertia, and the condensate fraction of an interacting quasi-two-dimensional trapped Bose gas with up to N∼5x10⁵ atoms and parameters closely related to recent experiments. We locate the Kosterlitz-Thouless temperature T_KT and discuss intrinsic signatures of the onset of superfluidity in the density profile. Below T_KT, the condensate fraction is macroscopic even for our largest systems and decays only slowly with system size. We show that the thermal population of excited states in the transverse direction changes the two-dimensional density profile noticeably in both the normal and the superfluid phase