This is a tough one, as Dany doesn't necessarily fit any of these roles. She isn't really a hero, as there aren't many sacrifices she has to make. Though, if you want to consider the idea she had to give up her virginity (originally as a step to get her brother closer to the throne), her brother (to reach her own potential), ever having children again (to save Drogo, though it didn't work and it was unwittingly done), and those she trusted most (Jorah, though he wasn't innocent) in order to keep her focus toward sitting on the Iron Throne, which she sees as her destiny - all of those things could be considered sacrifices worthy of a hero.
But because ASOIAF is so sprawling in its characters, people could view others as the hero of the story (though I would argue there are no heroes). Therefore, Dany could be a Threshold Guardian in waiting - she can ultimately be what stands between the hero and their chance to sit on the Iron Throne.
She could also be considered a Shapeshifter. She began the series as a meek, submissive child who had been controlled and manipulated for most of her life. She was oppressed by her brother and then dominated by Drogo. Ultimately, she transformed into a confident, strong, and focused young woman who is far wiser than most believe her to be. She has risen to the title of Queen of Westeros, which she has taken for herself and she is now strong enough to do what is necessary to achieve the goal of sitting on the Iron Throne.