The B(E2; I-i -> I-f) values for transitions in Ga-71(31)40 and Ga-73(31)42 were deduced from a Coulomb excitation experiment at the safe energy of 2.95 MeV/nucleon using post-accelerated beams of Ga-71,Ga-73 at the REX-ISOLDE on-line isotope mass separator facility. The emitted gamma rays were detected by the MINIBALL gamma-detector array, and B(E2; I-i -> I-f) values were obtained from the yields normalized to the known strength of the 2(+) -> 0(+) transition in the Sn-120 target. The comparison of these new results with the data of less neutron-rich gallium isotopes shows a shift of the E2 collectivity toward lower excitation energy when adding neutrons beyond N = 40. This supports conclusions from previous studies of the gallium isotopes, which indicated a structural change in this isotopic chain between N = 40 and 42. Combined with recent measurements from collinear laser spectroscopy showing a 1/2(-) spin and parity for the ground state, the extracted results revealed evidence for a 1/2(-), 3/2(-) doublet near the ground state in Ga-73(31)42 differing by at most 0.8 keV in energy.