Context. The role of bipolar jets in the formation of stars, and in particular how they are launched, is still not well understood. Aims. We probe the protostellar jet launching mechanism, via high resolution observations of the near-IR [Fe ii]λ1.53,1.64 µm emission lines. Methods. We consider the case of the bipolar jet from Classical T Tauri star, DO Tau, and investigate the jet morphology and kinematics close to the star (within 140 au), using AO-assisted IFU observations from GEMINI/NIFS. Results. We find that the brighter, blue-shifted jet is collimated very quickly after it is launched. This early collimation requires the presence of magnetic fields. We confirm velocity asymmetries between the two lobes of the bipolar jet, and also confirm no time variability in the asymmetry over a 20 year interval. This sustained asymmetry is in accordance with recent simulations of magnetised disk-winds. We examine the data for signatures of jet rotation. We report an upper limit on differences in radial velocity of 6.3 and 8.7 km s −1 for the blue and red-shifted jets, respectively. Interpreting this as an upper limit on jet rotation implies that any steady, axisymmetric magneto-centrifugal model of jet launching is constrained to a launch radius in the disk-plane of r0 < 0.5 and 0.3 au for the blue and red-shifted jets, respectively. This supports an X-wind or narrow disk-wind model. However, the result pertains only to the observed high velocity [Fe ii] emission, and does not rule out a wider flow launched from a wider radius. We report detection of small amplitude jet axis wiggling in both lobes. We rule out orbital motion of the jet source as the cause. Precession can better account for the observations but requires double the precession angle, and a different phase for the counter-jet. Such non-solid body precession could arise from an inclined massive Jupiter companion, or a warping instability induced by launching a magnetic disk-wind. Conclusions. Overall, our observations are consistent with an origin of the DO Tau jets from the inner regions of the disk.