No, copy editing is not one word in AP style (Associated Press Style). The Associated Press Stylebook prescribes a two-word spelling of the term—copy edit— rather than the one-word spelling of copyedit. It is always preferable to use the two words in a news article.
However, this rule may be relaxed in casual writing, particularly when space is limited (such as in a headline). In such cases, copyedit may be used.
It is important to note that other sources (e.g., the Chicago Manual of Style) may prefer the one-word spelling of the term. You should always refer to the appropriate style book for definitive guidance on the spelling of any words.