His ko, rather.
But she has ridden Drogon, and Rhaegal and Viserion are loose via Quentyn Martell. They are and always were smaller than Drogon, but even Barristan Selmy knows if you restrict dragons they will not grow as large.
It is definite that Tyrion Lannister knows this, too, hence the Red Priest of R'hollor's prophesy that he would live, to see 'Dragons old and new, and you in the middle, snarling.'
Will they respond to her or the horn Euron gave to Victarion? Rhaegal and Viserion look for their mother, according to the last of Quentyn Martell. He sees their eyes searching the other girl and realises they are looking for Dany.
She is the one, who figured out that telling them 'Dracarys' in her voice called them to release dragonfire, as before that she was chopping up their meat and charring it on a brazier. She introduces her find to Jorah when they set sail for what became Astapor. Though her Dothraki call it out, at the close of the books it appears at least Drogon responds only to her voice.
Then there's the whole R'hollor thing, and Martin has said the next book is going further north. The R'hollor priests and priestresses have all spoken of the other threat, whose name cannot be spoken, and Osha was about how Robb was marching the wrong way, that the real threat was from beyond The Wall.
But Targaryen is blood and fire.
Daenrys comes of VERY strong in the books. But so does Jon Snow. Little do we know of Aegon but Varys says he is for the realm not himself, and he does go against Lord Jon Connington. He makes a break, and goes to march to King's Landing, and that his aunt can meet him there.
If I had to wager, it is Dany, Aegon and Jon Snow to ride, Tyrion as Lord of Casterly Rock with his wife, Sansa Stark, who is already wising up, Bran as lord of Citadel, Rickon as head of Kingsguard, Arya as Lady of Winterfell.