The active ingredient, iodine, is safe for use around rabbits. Povidone iodine (diluted) can be used to disinfect wounds. I would not use the product above for that purpose, since it's not designed for that. It should not be ingested, though residue should have low toxicity.
I find that the best surface disinfectant is good old rubbing alcohol (isopropanol). Squirt it onto the surface, wipe it down to wet all surfaces, and allow to dry. The drying action is what kills the bacteria. Since most of it evaporates quickly, there is no toxic residue to worry about.
I've lived with companion rabbits for more than 35 years, and consider them members of my family. I can answer any questions about the biology and health of rabbits, from the commonplace to the unusual. But please note:
RULE #1: THE INTERNET IS NOT THE PLACE TO SEEK HELP IN AN EMERGENCY.
If your rabbits is LETHARGIC
If your rabbit is NOT EATING
If your rabbit is PHYSICALLY INJURED (including broken bones)
I have been rescuing and rehabilitating domestic and wild rabbits for about 30 years.
I have written articles for many rabbit rescue publications, as well as for the veterinary journal, Exotic DVM.
I own EtherBun, the internet's largest listserve dedicated to health, care, and behavior of domestic rabbits.
Organizations Houserabbit Adoption, Rescue, and Education, Inc. (H.A.R.E., Inc.) president
National House Rabbit Society (Board member)
Publications Exotic DVM
Warren Peace (Journal of the House Rabbit Society of Miami)
Various newsletters of the House Rabbit Society, nationwide
Education/Credentials Ph.D - Biology
B.S. - Biology
B.A. - English
Awards and Honors Lightspan Academic Excellence Award for web site on rabbit health and biology