Diffusivities and viscosities of poly(ethylene oxide) (PEO) oligomer melts of 1 to 12 repeat units have been obtained from equilibrium molecular dynamics simulations using the TraPPE-UA force field. The simulations generate diffusion coefficients with high accuracy for all molecular weights studied, but statistical uncertainties for the viscosity calculations significantly increase for longer chains. There is in good agreement of calculated viscosities and densities with available experimental data. The simulations can be used to fill in gaps in the data and for extrapolations with respect to chain length, temperature and pressure. We have explored the convergence characteristics of the Green-Kubo formulae for different chain lengths and propose minimal production times required for convergence of the transport properties. The chain length dependence of transport properties suggests that neither Rouse nor reptation models are applicable in the short-chain regime investigated.