Rhaega and the Ring; A Lord of the Rings/Game of Thrones AU Fanfiction

AUTHOR'S NOTE: None of my published works are very good (in my opinion), but I really appreciate everyone's kindness and support, so even though I'm a little embarrassed by my old stories, I'm leaving them up. Some of my works are already complete, and some are not. The ones that are incomplete will not be updated again, sorry, and thanks. :)
Khal Drogo and his Khaleesi have given birth to a little girl, a Khalakka named Rhaega.
When she is grown, Rhaega and her parents are called by Lord Elrond of Rivendell to discuss the fate of the the One Ring.
Taking the opportunity to prove herself to her father and her people, Rhaega embarks on the journey, becoming the tenth member of the Fellowship of the Ring.