As was later revealed in the reunion films I Dream of Jeannie... Fifteen Years Later (1985) and I Still Dream of Jeannie (1991), Jeannie and Tony did have a son whom they would name Tony, Jr. (TJ for short). However, they never had the daughter Jeannie, Jr. also foretold by Haji.
In this episode you can see a lot of Larry's input in the script. ( He directed the episode)..Jennie is a great cook, sews her own clothes, weaves a rug, and builds addition to the house. These were the same things Larry's wife "Maj" did.