When is it safe to use adult moisturizer on my baby's skin?

Anytime. The only difference between an "adult" moisturizer and a "baby" moisturizer is the labeling. Just be sure to apply it to a small area of skin the first time or two, to be sure that your baby is not allergic to or irritated by any of the moisturizer's ingredients.
Depends... ...What's in the moisturizer that makes it adult? If it's perfume, she can use it before her first date. The basic ingredients -- mineral oil, water, emulsifier -- are the same for all kinds of moisturizer; proportions determine how "gooey" the product is -- and preference for that varies more by skin type than by age.