Using femtosecond time- and angle-resolved photoemission spectroscopy we investigate the effect of electron doping on the electron dynamics in Ba(Fe_{1-x}Co_x)_2As_2 in a range of 0 < x < 0.15 at temperatures slightly above the N\'eel temperature. By analyzing the time-dependent photoemission intensity of the pump laser excited population as a function of energy, we found that the relaxation times at 0 < E-E_F < 0.2 eV are doping dependent and about 100 fs shorter at optimal doping than for overdoped and parent compounds. Analysis of the relaxation rates also reveals the presence of a pump fluence dependent step in the relaxation time at E-E_F = 200meV which we explain by coupling of the excited electronic system to a boson of this energy. We compare our results with static ARPES and transport measurements and find disagreement and agreement concerning the doping-dependence, respectively. We discuss the effect of the electron-boson coupling on the energy-dependent relaxation and assign the origin of the boson to a magnetic excitation.
