This post is probably kind of late, but the points are still technically relevant.
Kim Kyong-Hui is Kim Jong-Il's sister. Kim made her was named a general on the same day as his son, and she plays an instrumental role in the day-to-day functions of the government by serving on a number of important committees and is also one of Kim Jong-Il's closest and most trusted advisors. She seemed like a natural choice to fill the role after the crash.
Technically, Jang Sung-Taek, her husband, taking over would be just as likely, if not more, but your scenario works as well. I also thought that you opened up North Korea too quickly, but as we know almost nothing about the country, it's really your choice.
I don't know if South Korea has any female politicians.
I'm not sure if you meant this in a specific or general sense. South Korea certainly has female politicians, and the most popular is Park Geun-Hye, who is the daughter of the former deceased president Park Chung-Hee. She narrowly lost to Lee Myung-Bak in the primaries, and is still considered to be the favorite to win the presidential election this year, as each president is only allowed to serve one five-year term.