Semi-insulating iron-doped gallium nitride (GaN:Fe), a promising material for microwave electronics and optoelectronics, is characterized by means of current-voltage curves measured under non-equilibrium charge carrier injection conditions. To increase the electric field and enable local characterization of GaN:Fe, measurements are performed using a two-electrode configuration including a point contact with a diameter of 30 μm and large-area alloyed counter contact. Experimental evidence for various radial flow regimes corresponding to the universal 3/2 and quadratic power laws and to the so-called trap-filled-limit is presented. Furthermore, it is shown that the space-charge-limited current injected from the point contact may serve as a probe to measure both local and average scale density of electrically active traps, i.e., parameters that are necessary for GaN:Fe to be applied and optimized.