Dany is 17 at the beginning of the show. She is in fact the reason Robert's Rebellion was pushed back so it took place 17 years before the death of Jon Arryn, instead of 13 years before as it was in the books. This was because they needed an older actress to play the sex scenes with Drogo; any younger and it'd have been technically child pornography. Heck, they couldnt even have had a 17 year old play a 13 year old since it would still have been child pornography in some countries. And they knew Dany's sexual awakening with Drogo was an essential aspect of her character. So they aged her up instead.
Source:
http://youtu.be/QTTW8M_etko (Min 28. Some mild series spoilers in the video ).