To be perfectly honest, I am not crazy about her for Dany.
She's a very pretty young lady... but that's the problem. She looks like a young lady and not a young girl. I understand that you are aging Dany up a bit (from 13 to 15 is the rumor I heard), and that's understandable, and with the sexuality, obviously you had to have someone over 18 play her. But she does not look like a 15 year old. She looks like a 19-20 year old. Personally, I found one of the importances of Dany is her youth. That is an essential key element to her. There's such a mix of childhood innocence and raw power broiling underneath. Without that sense of childlike innocence and vunerability, the character looses so much.
Miss Merchant looks like she probably could have played Dany effectively at one point, but she simply doesn't look young enough to be convincing to me.
However, you are the author and if you are pleased with the casting choice then that is what matters. I will just wait and hope that she is able to bring this very important role to justice.