Dingoes weren't introduced. They originate in southeast asia, but they are very definitely our apex predator. They're actually important to the ecosystem. Livestock owners consider them pests because they attack their animals, but they're definitely not an introduced species like the fox or rabbit.
The 'dingo ate my baby' thing is from the case where a little girl by the name of Azaria Chamberlain was killed by a dingo. Her mother was accused and wrongfully convicted with her murder as authorities at the time didn't think an animal typically shy of humans could do such a thing. Keep in mind, that was in 1980, and her mother is now free as they eventually founds items of the girl's clothing in a dingo's den.