your area is completely without birds of prey? that’s surprising. and you can’t count on predators behaving around prey. your dog is also a predator. he may be trained to leave the rabbit alone, but that doesn’t mean you should leave them together unsupervised.
is your rabbit not used to being handled? are you rough when putting him in the cage?
Second poop today was just as it should be. Brown and solid. No lethargy or vomiting. He’s crazy happy, thorn his new bed apart, ate the whole lunch and snack. I am so happy that he’s alright!