My rabbit's dog bite wound has pus, redness, and hair loss. What now?

Poor Sunny D! Pus and redness are common signs of infection, which may require treatment with oral antibiotics. Dilute chlorhexidine is okay to use on the wound, as well as silver sulfadiazene ointment. I would steer away from triple antibiotic ointments such as Neosporin, as rabbits can ingest these during grooming and result in gastrointestinal upset. From the picture, the wound appears to be closing, which is a good sign. I recommend monitoring the wound for another day or so, and having Sunny D seen by a vet if the discharge continues to get worse. Sunny D may also require some pain medication, that can only be prescribed by a vet. In the meantime, you can also get him a small E-collar or "cone" to prevent him from scratching the area. He may need the cone removed for a few hours while you supervise him closely in case he is not comfortable eating in it. I hope this helps and that Sunny D starts feeling better soon!