Shannon entropy (S), Fisher information (I) and a measure equivalent to Fisher-Shannon complexity (C-IS) of a rovibrational state of diatomic molecules (O-2, O-2(+), NO, NO+) with generalized Kratzer potential is analyzed. Exact analytical expression of I-r is derived for the arbitrary state, whereas the same could be done for I-p with {n, l, m = 0} state. It is found that shifting from neutral to the cationic system, I-r increases while S-r decreases, consistent with the interpretation of a localization in the probability distribution. Additionally, this study reveals that C-IS increases with the number of nodes in a system.