。
She went out with her dog.
Literal
She [topic-は] dog [object-を] taking-along went-out.
連れる ('to take along, bring with') is the verb you reach for when the companion is a person, child, or animal you're shepherding (rather than an equal you'd join with と). Here it links to 出かける ('to go out, head out') via the て-form, building a sequential 'took the dog along, then went out.' English collapses this into 'went out with her dog,' but the Japanese makes the shepherding action explicit. 連れて出かける and 連れて行く are both common; the former emphasizes leaving the house, the latter the destination.