The statement that exemplifies wordplay is:
“Well, yes, if you call that a-dressing,” The Queen said. “It isn't MY notion of the thing, at all.”
In this sentence, the term "a-dressing" plays on the word "addressing," as Alice is trying to engage the Queen in conversation, but the Queen interprets Alice's wording as relating to physically dressing herself. This clever use of language creates a humorous misunderstanding between the characters.