There's also a sign (on the wall) that says "Quiet Sleeping". There aren't any other child actors, so Juli's the only person on set who needs to attend school, and with that, the 'sleeping' sign and the star on the door I'd say it's more likely her dressing room.
I've seen this picture on an Icelandic news site before. There's 2 versions it seems, but it's just tilted at an angle. Here's a bunch of pictures I stole from that website, http://www.visir.is/apps/pbcs.dll/frontpage :
hm, it all makes sense now. Cause I remember her mentioning doing school work when she had time in between filming...yeah that's her dressing room for sure then! ONE MYSTERY SOLVED ONE MORE TO GO!
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