Oh, right! I knew it was a moon they were on, then promptly forgot it and saw it as a planet, haha.

These are a lot of great options! I like the idea of her transformation being tied to whenever the planet sees this moon as full. Could I just make it every full moon on our real world calendar for ease of remembering it?

As for where she'd shift, I can see her trying to work out a place for herself before she would spill her secret to the people in charge, so going into the forest would work for her needs. Are people allowed outside the wall whenever they want, or would she be questioned a lot about her intentions?