Depends on what you consider as "adult"
Today people are considered adults at 18, but I wouldn't trust an 18yr old to do most adult like things, such as successfully buying a car, getting quotes on different insurances, things like that.
If you're wanting them to be technically classified as an adult then yup I'd say 18 is right on the money. If you want them to be a more "worldly" adult then I'd shoot for someone in their mid 20s. So its all really up to you in how you feel about your character or what you're hoping to accomplish with her.