Get her out the camp and take her where? Off to die in the snow?
Look I've conceded it's possible he doesn't know, we'll see next episode. But they've definitely hinted to the viewer that he knows. Maybe those hints were meant to be just foreshadowing devices for the viewer, but by having Davos snicker at Mel and then plead with Stannis to let Shireen stay at Castle Black, it suggest that Davos knows Shireen is in danger. That is then reaffirmed when Stannis is facing his darkest hour and clearly prime for reaching out to the Lord Of Light, and Davos pleads to have someone else sent to Castle Black and then IMMEDIATELY brings Shireen up out of nowhere. That suggests he knew she was in danger.
But it's fiction so if they say he didn't know then he didn't know