Craig Lunn, the Tararua District Council's manager of regulatory services, confirmed the after-hours animal control officer had been called out at 11pm to the dog attack.
An investigation is being carried out and the dog has been impounded, he said.
Jackson said the dog jumped a 1.8 metre high fence to get to Nitro.
"It's so frustrating and this has all become too much," she said.
Animal control officers installed a CCTV camera at the Matthew St property and an electric fence around cages, but Jackson said the attack still happened.
"Council have told me they are looking at prosecuting the dog owner through the courts and I'm putting together an impact statement, so I hope the prosecution goes ahead," she said.
"But my biggest concern is that while court action may stop this dog, what is there to stop the owners getting other dogs?"
In 2017 the Jacksons' pet goat Queenie was attacked by two dogs.
The family had owned goats Queenie and Chocco for seven years, giving them a loving home when they were just a few days old. They were much loved by all the members of the family, especially sons Andreas and Anton.
However, in order to keep the goats safe the family had to make the tough decision to have them rehomed.
They have assimilated well with other goats they now live with.