When you do read the books, one of the things you'll notice is that legend and prophecy play a much larger role than they do in the TV series. We've gotten glimpses of them, sure, but only glimpses. The Red Comet, seen only in S02E01 of the TV series but referenced throughout the books; Bran Stark and Jojen Reed's "greensight" visions, especially of the Three-Eyed Crow; the prophecies about R'hllor and Azor Ahai, a.k.a. the Lord of Light and his flaming sword-wielding messiah (Stannis Baratheon? Beric Dondarrion? or is it a metaphor for something else?); the legends of the First Men and their dealings with the native, non-human races; the legends of House Targaryen, Old Valyria, and the Doom; and most relevant to your thoughts about Daenerys, the true power of the Warlocks of Qarth in the House of the Undying.
In the second book, A Clash of Kings, the House of the Undying sequence is much longer and more complex and provides many more visions of Dany's past and future. That gives her a greater sense of destiny, which propels her through the third book, A Storm of Swords. That's what you're seeing now in the TV series, unfortunately without the full context.