Craik is correct in this surmise. The Maori dog, Canis familiaris, (Variety Maorium), which is now extinct, was introduced to New Zealand when the Maoris came at the time of their great migration, about 500 years ago.
The alligator is purely mythical. The only reptiles in New Zealand are lizards, and a lizard-like animal called Tuatara. It is about 18 inches long, and is allied to crocodiles and turtles, as well as lizards. It is the sole representative of an ancient reptilian order named Rhyncocephalia.
This is the bell-bird (Anthornis melanura).