Not just Tularemia; people can contract Leptospirosis - not a fun thought; rabbit tapeworm can be spread to the dogs. Coccidiosis, Giardiasis, Cryptosporidiosis; so many reasons to keep our dogs away from 'cute little bunnies'.
The mother rabbit only stays with the babies for about 5 minutes at a time to nurse them; then she goes out to forage. People, well-meaning people, assume that the babies have been abandoned. Mom will come back in her own time.
When we raised domestic rabbits we had to learn all this stuff. As cute as the wild rabbits may be, they are still vermin. I hate to say that, but it's true.
Dogs like to lick and eat things like rabbit poop and urine - hey, they're dogs; it's what they do. If the dogs are quick enough they can kill a rabbit thus coming into contact with the flesh, blood and intestinal stuff. Yuck. Our first responsibility is to our family and to our family dogs, not to the wild rabbits.
When we first tried to raise domestic rabbits (before we got serious and studied), we lost our entire population of rabbits to Enteritis. Very messy and not fun. We delivered one dead rabbit to the University of Connecticut to obtain a positive diagnosis. Dogs can catch this and it is often fatal.
http://www.medirabbit.com/EN/G...
(Sheesh, I sound so serious!
Sorry. Feel free to ask me to edit or delete the bad stuff if it offends, okay?)