Ionic conductivity and water transport through alkaline Anion Exchange Membranes (AEM) are key properties for application in Alkaline Membrane Fuel Cells (AMFC), Redox-Flow-Cells, or Alkaline Membrane Electrolysis. AEMs consist of a polymer domain with cationic side groups and a pervading water domain through which anions are conducted. In this study, Quasielastic Neutron Scattering (QENS) is employed to study water rotational and diffusive dynamics in the hydroxide form of a model AEM (Fumatech FAA-3) at water contents relevant for application. Two distinct diffusion time-and length-scales are accessed: "Localized" diffusion at the lower Angstrom/tens of picosecond scale and "extended" diffusion at the higher Angstrom/hundreds of picosecond scale. The localized diffusion length scale is smaller than the membrane's water domain thickness and its diffusion coefficients remain close to the value of bulk water even at decreasing water content. Extended diffusion approaches the thickness of the water domain and its diffusion coefficients decrease strongly with decreasing water content. A master curve links water domain thickness to the extended water diffusion coefficients for the alkaline hydrocarbon model AEM and literature data on acidic per-fluorinated Proton Exchange Membranes.