My mother has just this moment gone out shopping.

Literal

Mother [topic-は] just-now shopping [purpose-に] went-out-[completive-てしまいました]

たった今 = 'just this moment' — even more immediate than ちょうど. 出かけてしまいました = 'has (unfortunately) gone out.' てしまう here expresses slight regret or inconvenience — she's just missed, the person asking is too late.