We use resonant elastic and inelastic x-ray scattering at the Ir-L₃ edge to study the doping-dependent magnetic order, magnetic excitations, and spin-orbit excitons in the electron-doped bilayer iridate (Sr_1-xLa_x)₃Ir₂O₇ (0 ≤ x ≤ 0.065). With increasing doping x, the three-dimensional long range antiferromagnetic order is gradually suppressed and evolves into a three-dimensional short range order across the insulator-to-metal transition from x = 0 to 0.05, followed by a transition to two-dimensional short range order between x = 0.05 and 0.065. Because of the interactions between the J_eff = ½ pseudospins and the emergent itinerant electrons, magnetic excitations undergo damping, anisotropic softening, and gap collapse, accompanied by weakly doping-dependent spin-orbit excitons. Therefore, we conclude that electron doping suppresses the magnetic anisotropy and interlayer couplings and drives (Sr_1-xLa_x)₃Ir₂O₇ into a correlated metallic state with two-dimensional short range antiferromagnetic order. Strong antiferromagnetic fluctuations of the J_eff = ½ moments persist deep in this correlated metallic state, with the magnon gap strongly suppressed.