She was doing the laundry at the time.

Literal

She [topic-は] that-time laundry [object-を] was-doing.

洗濯をする ('do the laundry,' lit. 'do washing') is a common light-verb construction — 洗濯 as the noun, する as the verb, with optional を marking the noun as object. その時 ('at that time') is a temporal noun used here without a particle, common in narrative — Japanese often allows time references to stand alone, with their position making the function clear. The progressive ~ていた frames the action as ongoing at the past reference moment.