As I am informed iodine is mostly in seafood , in very minimal amounts in vegetables and in high dose in salt with added iodine..
try to scroll the links page, down the page is a section that tells ; Allowed Foods and Ingredients http://www.thyca.org/pap-fol/lowiodinediet/
egg whites and unsalted nuts and fresh meat without added salt ,seems to be the only choices...
but this alone can not make a whole diet.. can you eat berries ?