Can you tell me if it's likely that a rabbit scratch could become infected?

It is possible.: Rinse wound w clean water. Clean surrounding skin w soap & water on wash cloth. Apply antibiotic ointment. Initially cover w bandage until some healing has occurred. Change bandage when soiled/ wet or at least daily. Need tetanus shot if you haven't had one in last 10 years, don't know when you last had one or if the wound is dirty & it has been more than 5 years since last shot.