About does not need an object: "Looking about" is the same as "looking around". For example: according to an 1841 report on British prisons (which you can find with Google), a prisoner could be denied supper for "constantly looking about"... Perfectly good translation to "mirar alrededor".
Just a question: when I was learning Spanish growing up, I was always taught to say (in a sentence like this) "ella mira a su alrededor" because the emphasis was on looking around one's immediate vicinity. "Ella mira alrededor," the "correct" Duolingo translation, sounds a little funny to me...thoughts?
"The alveolar trill [r] and the alveolar tap [ɾ] are in phonemic contrast word-internally between vowels (as in carro 'car' vs caro 'expensive'), but are otherwise in complementary distribution. Only the trill can occur after /l/, /n/, or /s/ (e.g. alrededor, enriquecer, Israel), and word-initially (e.g. rey 'king'). After a stop or fricative consonant, only the tap can occur (e.g. tres 'three', frío 'cold')."