She set out on a journey last week.

Literal

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

昨週 ('last week') is a less-common written variant of the everyday 先週 — both mean the same thing, but 昨 (the same kanji as in 昨日 'yesterday' and 昨年 'last year') carries a slightly more literary, written-register feel. 旅 is the older, more poetic word for a journey; 旅行 is the modern, neutral 'trip.' 旅にでる ('set out on a journey') matches that elevated register — bashō and the wandering-poet tradition lurk behind the phrase. The に here marks 旅 as the purpose or destination of でる ('go out').