**Edit**: I took "The dog barked at nothing" as "The dog barked at a place where there is nothing."
Sorry if I have misunderstood.

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I think there is no word in Japanese that exactly matches that "nothing."
So you have to describe the situation more concretely.
For example:

> 犬が**何もない所に向かって**吠えた。  
> The dog barked at nothing.

Here, 「Aに向かって吠える」 is a typical translation of "bark at A".
And 「何もない所」 is "the space where nothing exists."

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Maybe, the word 「[虚空]{こくう}」 (== empty space) is closer:

> 犬が**虚空**に向かって吠えた。

But this word sounds literary; not used in daily conversations.

Or 「[無]{む}」 may express the idea of nothing being existing (cf. 無を取得) but it sounds too paradoxical and less natural.