Unfortunately, you won’t get iodine from yogurt. In fact, short of eating massive amounts of kelp every day like they do in Japan, you won’t get enough to offset the toxic halide Bromine, that is in almost all of our baked goods, including a ton of other non edible products.
You have to supplement with it and the only 2 products that have the right amounts of iodine/iodide are Iodoral (pill form) or Lugol’s (liquid).
Now that you said that I’m curious about the breast cancer rates among the Japanese women.
I actually found a recipe that combines yogurt and seaweed. I’ve thougth about making it and posting it on my blog. LOL!