We have measured the nascent HD(v' = 1,j') product rotational distribution from the reaction D + H-2(v, j) in which the H-2 reagent was either thermal (v = 0, j) or prepared in the level (v = 1, j = 1) by stimulated Raman pumping. Translationally hot D atoms were obtained by uv laser photolysis of DBr or DI. Photolysis of DBr generated D atoms with center-of-mass collision energies (E(rel)) of 1.04 and 0.82 eV, which corresponded to the production of ground state Br and spin-orbit-excited Br*, respectively. The E(rel) values for DI photolysis were 1.38 and 0.92 eV. Quantum-state-specific detection of HD was accomplished via (2 + 1) resonance-enhanced multiphoton ionization and time-of-flight mass spectrometry. Vibrational excitation of the H-2 reagent results in substantial rotational excitation of the HD(v' = 1) product and increases the reaction rate into v' = 1 by about a factor of 4. Although the quantum-mechanical calculation of Blais et al. [Chem. Phys. Lett. 166, 11 (1990)] for the D + H-2(v = 1, j = 1) --> HD(v' = 1, j') + H product rotational distribution at E(rel) = 1.02 eV is in qualitative agreement with experiment, it does not quantitatively agree with the measured distribution. Specifically, the calculated distribution is too hot by 2-3 rotational quanta, and the predicted enhancement in the v' = 1 rate with reagent vibrational excitation is too large by 67% +/- 9%.