The structural and dynamic properties of low ionic strength micellar solutions of the cationic surfactant perfluorooctylbutane trimethylammonium bromide have been investigated by means of dynamic and static light scattering and rheological experiments. In the range of concentration extending from the critical micelle concentration to about the overlap concentration, the surfactant self-assembles into micellar aggregates with sizes of the order of 100 nm. At higher concentrations, the system is characterized by a single correlation length consistent with the formation of a transient network of wormlike micelles. In the dilute regime, the solutions exhibit a very large shear thickening effect (up to 50) and a very slow recovery (hours) after a thermal or mechanical perturbation. The extent of consistency of the dynamical observations with the various possible structures inferred from the scattering data has been discussed. Some arguments are in favor of the presence of interlinked micellar rings in the quiescent state, which was suggested in a recent theoretical model.