Being wrongfully sued for a dog bite. The dog is not mine.

What are you counter claiming? If the dog is not yours, you show up at the hearing with proof the dog is not yours and ask for the suit to be dismissed. Or you can file for a dismissal before the hearing. Why does the plaintiff think the dog is yours.

First, OP should file a written answer with the court, stating that the dog is not OP's and OP did not cause the injury. To answer the question OP asked, a counter-claim would be included in this "answer" (although, like Scott-Gem, I don't see why a counter-claim would be warranted). This answer should be filed within the time specified in the summons (normally about 20 days).

If a hearing is scheduled, then, OP should show up and be prepared to prove that the dog was not his/hers.

Once you prove the dogs not yours and win, can the judge for Judgment against the plaintiff for you time and expense