Okay she's not a King, but she's the mother of dragons and bathes in fire...so she instantly gets a bid to the iron throne.  Also being a woman, she probably can communicate better then all the other lords :)
 
She is the only surviving child of King Aerys II Targaryen who was ousted from the Iron Throne during Robert's Rebellion. She lives in exile in the East. Daenerys was married to the Dothraki Khal Drogo but lost her husband and unborn son to the manipulations of the vengeful maegi Mirri Maz Duur. Her marriage to Drogo and subsequent interaction with the Dothraki people gives her the confidence to lead and the belief in herself as the rightful queen of Westeros. She plans to retake her homeland. She hatched three dragons by walking into Drogo's funeral pyre with the eggs. Hers are the first dragons seen in the world for hundreds of years.