The majority of planetary nebulae (PNe) show axisymmetric morphologies, whose causes are not well understood. In this work, we present spatially resolved kinematic observations of 14 Galactic PNe surrounding Wolf-Rayet ([WR]) and weak emission-line stars ($wels$) based on the H$alpha$ and [N II] emission taken with the Wide Field Spectrograph on the ANU 2.3-m telescope. Velocity-resolved channel maps and position--velocity diagrams, together with archival Hubble Space Telescope ($HST$) and ground-based images, are employed to construct three-dimensional morpho-kinematic models of 12 objects using the program SHAPE. Our results indicate that these 12 PNe have elliptical morphologies with either open or closed outer ends. Kinematic maps also illustrate on-sky orientations of elliptically symmetric morphologies of the interior shells in NGC 6578 and NGC 6629, and the compact ($leq 6$ arcsec) PNe Pe1-1, M3-15, M1-25, Hen2-142, and NGC 6567, in agreement with the high-resolution $HST$ images containing morphological details. Point-symmetric knots in Hb4 exhibit deceleration with distance from the nebular center that could be due to shock collisions with the ambient medium. Velocity dispersion maps of Pe1-1 disclose point-symmetric knots similar to those in Hb4. Collimated outflows are also visible in the position--velocity diagrams of M3-30, M1-32, M3-15, and K2-16, which are reconstructed by tenuous prolate ellipsoids extending upwardly from thick toroidal shells in our models.