。
She's drunk with happiness.
Literal
She [topic-は] happiness [in-に] is-intoxicated.
酔う ('to get drunk, to be intoxicated') has both literal (酒に酔う 'get drunk on sake') and figurative uses (幸福に酔う 'drunk on happiness,' 勝利に酔う 'drunk on victory,' 自分に酔う 'self-absorbed'). The figurative reading borrows the loss-of-control imagery from intoxication and applies it to overwhelming emotion. The に marks what the intoxication is on. The resulting-state ~ている here gives the ongoing condition of being drunk.