It seems to me that the Great Link is kind of like some mass communistic state. There are no leaders, and essentially all are equal. At least I sense amongst Changelings there are no senior or junior conspecifics. Even though Odo technically may have been younger than the Female Changeling, she did not deem him a junior or an inferior.
That said, could the Female Changeling in a way have been Odo's mother? It seems weird, but maybe the manner in which Changelings reproduce is that some members of the Link volunteer their DNA for copying or reassortment into a new Changeling. Maybe this is why it was the Female Changeling specifically who greeted Odo in The Search. It's a just a theory lol..