I would dearly love to bring Dany with at least one of her dragons, but the thing is her dragons aren't cute and tameable like Toothless and at least one of them has eaten someone, so they most likely will not be joining her.

It's gonna be a huge shock to the system at first, as it always is for a character that comes from a world without electricity and cars and the like, but one of her strongest assets in canon has always been her ability to adapt to a new culture and environment, so she'll get settled and do very well I think. :)