She set out on a journey last week.

Literal

She [topic-は] last-week journey [on-に] went-out.

旅に出る (たびにでる) means 'to set out on a journey' — more evocative and literary than 旅行に出かける. 旅 (たび) carries the weight of a longer, more meaningful journey compared to 旅行 (りょこう), which is the standard practical word for 'trip' or 'travel.' Think of the English distinction between 'journey' and 'trip.'