Kind of like Snakehead fishing here in Maryland. We can't eradicate the things because they breed five times a year and they lay a ton of eggs. It is against the law to catch and release them. You catch one, you kill it (they are good to eat).
Logic says that the larger an animal is, the easier it should be to eradicate. Fish are one thing, but emus, well, I'm guessing that if the Australian government decided on revanchism today, they'd be a lot more successful.