We numerically study the imprinting and dynamics of dark solitons in a bosonic atomic gas in a tightly confined one-dimensional harmonic trap both with and without an optical lattice. Quantum and thermal fluctuations are synthesized within the truncated Wigner approximation in the quasicondensate description. We track the soliton coordinates and calculate position and velocity uncertainties. We find that the phase fluctuations lower the classically predicted soliton speed and seed instabilities. Individual runs show interactions of solitons with sound waves, splitting, and disappearing solitons.