Personally, I think your best bet is electric poultry fencing. Premier has it and you can get it online. Chickens and rabbits bring out the prey drive in dogs and that is hard to overcome.
Just a comment. Buying a new rabbit is always cheaper, but sometimes it is helpful to know why the rabbit died. If you cut the rabbit open you can spot some conditions yourself. You can spot a twisted intestine or abnormalities in the liver and lungs for instance.
I miss having a dog. I am not really in a position to care for one now, but I really miss my Pugs. Pugs are wonderful companions. To me they also look like the result of a bad blind date between a gargoyle and a manatee.
Does the rabbit have any other symptoms? Runny nose? Abnormal abdomen? Like tight or squishy? Labored or rapid breathing? In my limited experience, taking a rabbit to a vet is an exercise in futility. You can spend a lot of money and still have a dead rabbit. Force feeding the rabbit is really...
Without seeing the goat it is difficult to have an opinion. If it was my goat I would immediately give her a dose of clostridium perfingens antitoxin. She may have enterotoxemia. If she does, you don't have much time. Another possibility is polio. Thiamin is used to treat that. If she has entero...
For what it is worth, I fed my dogs Purina Formula One. Meat is the first ingredient. They liked it and their stools were always firm and virtually odor free.