I mean, so far she doesn't give any indication to have a steadfast set of beliefs.
Most of the characters who aren't Ironborn or Northerners believe in the 7 faced god, right? Robert used to swear on them a lot.
The Northerners (including all the starks) and thus the wildlings are believers in the old gods; both Aeron and Victarion seem to be believers in the Drowned God and I even would go as far as to bet that so does Euron. But Dany doesn't seem inclined to any religious belief, and she doesn't seem to be an Atheist either.
Will she convert to a religion? like, i dunno, R'hollorism or any other.
Because a good bunch of religious characters seem to be interested in her.