We combine magneto-optical imaging and a magnetic field pulse technique to study domain wall dynamics in a ferromagnetic (Ga,Mn)As layer with perpendicular easy axis. Contrary to ultrathin metallic layers, the depinning field is found to be smaller than the Walker field, thereby allowing for the observation of the steady and precessional flow regimes. The domain wall width and damping parameters are determined self-consistently. The damping, 30 times larger than the one deduced from ferromagnetic resonance, is shown to essentially originate from the non-conservation of the magnetization modulus. An unpredicted damping resonance and a dissipation regime associated with the existence of horizontal Bloch lines are also revealed.