Sugar in milk and yogurt

Hello all, glad to find this site and forum. I read the book 'Potatoes not Prozac' years ago, then re-read it maybe a few months back and I'm determined to really kick the sugar cravings!

I've made a lot of progress, in that I've stopped lots of unnecessary sugar drinks (soda, icee, milkshake) and I no longer crave baked goods, cookies, (though I struggle still with ice cream!)

I was thinking that having regular yogurt instead, could help me get over the cravings for frozen yogurt and ice cream. But doesn't all dairy have sugar...and so, is yogurt and milk okay to consume?

I was thinking if the yogurt is non-fat, and the milk too, then it wouldn't be so bad to include in my diet, since the yogurt especially has good protein that could help a lot with step 1. Anyway, look forward to hearing your advice and suggestions!