China has a candy called White Rabbit - it's sort of like a vanilla taffy. The inner wrapper is made of rice paper and is totally edible.
You probably won't be able to find the White Rabbit. Several months ago, there were some milk suppliers in China who were purposely thinning out their milk before passing it along to manufacturers. What they were thinning it out with happened to be poison (melamine). A good portion of the milk went into baby formula. Many babies got sick, some died, and all milk products in/from China were recalled. White Rabbit is milk candy.
I celebrate Chinese New Year with my 8th grade students, and I go to asianfoodgrocer.com to buy Asian candies and snacks to let them try. In 2008, the White Rabbit was so popular the kids would bring me money to order the candies for them. My students this year were so upset that I couldn't order it for them, but I don't think they were disappointed with what they wound up getting instead. I still have not been able to find the candy, almost a year later.
Here is one article about it:
http://news.bbc.co.uk/2/hi/asia-pacific/7624969.stm (BBC dated September 2008). There were 3 people involved (I think). I remember that the woman involved got the death penalty. Google "China Milk" and you should find a lot about it, if you're interested.
All that said, Japan does have a few milk-based candies that are comparable, but none quite as good as White Rabbit, nor do they come in as many interesting flavors as White Rabbit did.