The title is a parody based upon the advice column Dear Abby, started by the late Abigail Van Buren and now carried on by her daughter. (Abigail's sister wrote a rival column, Dear Ann Landers.)
The title of the episode is a double pun in that it is not only a cultural reference to Dear Abby, but it is also a reference to what her type of column was called within the newspaper industry: "agony aunts". In this case, Aggie is as much a reference to Abby, as it is a diminutive of "agony" (as in "agony aunt").
The home setting is the same as the one used in I Dream of Jeannie. It is especially obvious with the greenish glass portion to the kitchen.