I wonder if the opposite of worry is expectancy. I'm sure somebody has written this somewhere, but it seems to me that worry just fills the person with fear of what lies around the corner. It consumes the person, drawing them into a cycle of "Oh no, what's going to happen next?".
But expectancy (maybe there is a better word for this) looks forward to what God is going to do. It trusts. It believes that God is a good God and will take care of Her beloved. Expectancy wants to see how God is going to make a difference and how God is going to affect the future.
While worry pines in the corner, expectancy prepares for the future.