We constructed a Hubble Space Telescope (HST) astro-photometric catalog of the central region of the Galactic globular cluster NGC 1261. This catalog, complemented with Gaia DR2 data sampling the external regions, has been used to estimate the structural parameters of the system (i.e., core, half-mass, tidal radii and concentration) from its resolved star density profile. We computed high-precision proper motions thanks to multi-epoch HST data and derived the cluster velocity dispersion profile in the plane of the sky for the innermost region, finding that the system is isotropic. The combination with line-of-sight information collected from spectroscopy in the external regions provided us with the cluster velocity dispersion profile along the entire radial extension. We also measured the absolute proper motion of NGC 1261 using a few background galaxies as a reference. The radial distribution of the Blue Straggler Star population shows that the cluster is in a low/intermediate phase of dynamical evolution.