We report on an inelastic light scattering study in the two-dimensional electron system at filling factor nu=1. The energy and the inelastic cross section of the cyclotron spin-flip mode are analyzed. The exchange enhanced electronic g factor in the quantum Hall ferromagnet is measured. In addition to the magnetoplasmon and cyclotron spin-flip modes, inelastic scattering lines associated with spin-singlet and spin-triplet D- complexes are observed. The inelastic light scattering is shown to probe the thermodynamics of the quantum Hall ferromagnet and gives insight into the formation of ferromagnetic order in two dimensions. It is established that at temperatures above the bare Zeeman energy, the ferromagnet breaks up into domains, whose size and number change with temperature. The experimental data allow us to construct a stability diagram of the nu=1 quantum Hall ferromagnet in the temperature versus magnetic field plane.