。
She goes for walks with her dog.
Literal
She [topic-は] dog [with-と] together walk does.
と一緒に doubles up the comitative と with the adverb 一緒に ('together') for emphasis — 'together with the dog.' Bare 犬と would be enough, but adding 一緒に foregrounds the togetherness; it's the most natural everyday way to say 'with someone/something' for a shared activity. 散歩する ('to take a walk') is a noun-plus-する compound, and either 散歩します or 散歩に行きます works equally well.