Vickie call the rabbit Blue, because it was blue. It wasn't really a rabbit strictly speaking, but it looked and felt like a rabbit and smelled like a rabbit. She let it out at night and it would disappear until dawn.
Her neighbor had too big dogs. They were real dogs from Earth. The neighbor would let the dogs loose and they would kill real rabbits all night for the fun of it.
Vickie found this repulsive. She wouldn't have minded as much, but the dogs would drag their catches home and leave rabbit pieces all over her lawn, which her neighbor would let rot if she didn't clean it up.
She began to hate those dogs. Then she read about the Blue. He was a babbit. Babbit's are genetically engineered to be cuddly and cute and blue. They only have one flaw. They hate dogs, and give them a more vicious treatment than a Badger gives a bear. They even chase the dogs, until the dog gets away, or the Babbit gets the dog.
So now every night she would let Blue out, just after the neighbor let his dogs out. When the dogs had never seen a Blue before, they thought that it would be fun to spread blue over a few lawns.
Both dogs survived, but they ran away and didn't come home for two days. Vickie had to laugh at that. Eventually they learned to hide when Blue was let out for the night, and they would come out of hiding when the Blue was taken inside in the morning.
The neighbor came over one day a few weeks after Vickie had bought blue. Vickie was sure that he would yell at her about how Blue treated the dogs, but to her surprise, he bragged to her that he had finally trained his dogs not to kill rabbits senselessly.
Vickie managed to not roll her eyes, somehow. Either way, the rabbit killing spree came to an end, and that was her goal, so she was happy.