。
She's writing something in the study.
Literal
She [topic-は] study [in-で] something writing is-doing.
書き物をしている uses the compound noun 書き物 (writing/written work) with をする (to do) plus ~ている for an ongoing action. 何か (something) is deliberately vague — the speaker doesn't know or isn't specifying what she's writing. 書斎 (しょさい) is specifically a study or home office used for reading and writing — a more specific room than just 部屋.