。
She wants a new hat.
Literal
She [topic-は] new hat [object-を] is-showing-desire-for.
欲しがる follows the same pattern as ~たがる — Japanese uses ~がる to express a third person's desires as observed from the outside. While 欲しい (first-person: 'I want [object]') marks its object with が, 欲しがる (third-person: 'shows signs of wanting') takes を. This particle shift reflects the grammatical change from an adjective (欲しい) to a verb (欲しがる).