The local structure of correlated spin-orbit insulator Sr2-xMxIrO4 (M = K, La) has been investigated by Ir L3-edge extended X-ray absorption fine structure measurements. The measurements were performed as a function of temperature for different dopings induced by substitution of Sr with La or K. It is found that Ir-O bonds have strong covalency and they hardly show any change across the Néel temperature. In the studied doping range, neither Ir-O bonds nor their dynamics, measured by their mean square relative displacements, show any appreciable change upon carrier doping, indicating the possibility of nanoscale phase separation in the doped system. On the other hand, there is a large increase of the static disorder in Ir-Sr correlation, larger for K doping than La doping. Similarities and differences with respect to the local lattice displacements in cuprates are briefly discussed.