Would it look weird if a 15 year old walked around with this clinging to her back?

Domo is pretty popular, and it's pretty cool. Stores like hot topic carry domo merchandise and it would not be considered odd for you to wear it. It's more like a statement, wear that, and you are the kind of person who likes domo. Depending on the normalness of the rest of their wardrobe, it's likely fine.