DREAM OF
= to wish or to desire
She dreamed of having her own house.
"Dream of" is usually a preface to a statement which reflects something that someone hopes for, that they aspire to be, or that is a goal of theirs.
DREAM ABOUT
= to have a dream about sth while sleeping
She dreamt about food.
"Dream about" denotes something which someone had a dream about, a series of mental images or scenes that one experiences while they're sleeping.
However, the difference is so subtle that in my personal non-native opinion it's almost non-existing. And since I heard a lot of OF/ABOUT mixtures I treat it as one of those language nuances that you may or may not pay attention to :))
source: google images