Not all kennel cough is caused by bacteria. The type we have here is caused by a flu-like virus. Viruses don’t readily cross the species-barrier. They can do so, under special circumstances as with the 1918 Spanish Flu and the H1N1 flu of 2009-2010.
If the kennel cough is caused by bacteria, it’s most often bordetella bronchiseptica. Has the dog been put on antibiotics? Bordetella bronchiseptica is sensitive to Baytril (enrofloxacine) and to doxycycline. If the dog is being treated, the cough will persist longer than the infectious bacteria.
Chances are your bun already is a carrier of this bacteria, because it is very common among rabbits. B. bronchiseptica can cause illness in a bun, but a bun can also become an asymptomatic carrier and never show any signs of illness. Why some individuals get sick and others don’t, is not quite understood.
To be safe, direct contact with secretions from the dog (for examples droplets from sneezing or coughing) and the rabbit’s nose is best avoided. Keep the bun isolated from the dog, wash your hands carefully before you handle the rabbit and his cage and food etc. You can use a hand-sanitizer that has 70% ethanol (alcohol), because bordetella is sensitive to ethanol.
Bordetella bronchiseptica can cause snuffle-like problems. Symptoms are for example runny nose (mucus can be quite runny and clear, or thick, white and gloppy), coughing and sneezing, eye drainage, loss of appetite. If your bun gets sick, contact a vet for antibiotics and tell them about the dog’s kennel cough. Baytril is a bunny-safe antibiotics.