I'm not a fan of little dogs but Galak is a cutie.
This one is fairly iconic so it wasn't hard to find it at all - I recognized it right away. Alizee occasionally wears a white scarf with black skull print. It's from Alexander McQueen's scarf boutique.
Made from silk chiffon. Goes on the official site for $295.
You can buy one here:
http://www.alexandermcqueen.com/scar...?scarf3d=false
This particular color is "Ivory".