。
She added, as if it had just occurred to her, that she'd be going out shopping.
Literal
She [topic-は] later thought-of [as if-ように] shopping [object-を] do [for-purpose-に] go-out [explanatory-のだ] [quotative-と] added.
An intricate sentence stacking several patterns. 思いついたように ('as if just thought of') is an attributive ように clause modifying the manner of speaking. 買い物をしに出かける chains a purpose-に clause (買い物をしに 'to do shopping') onto a motion verb — same pattern as 食べに行く ('go to eat'). The whole embedded clause is wrapped with explanatory のだ + quotative と, then plugged into 付け足す ('to add as a remark'). The sentence reads like a snippet of careful narrative — the kind of thing you'd find in a novel describing offhand asides.