The dingo must have already been at least somewhat domesticated when it was brought to Australia (4-12,000 years ago, later than the first humans) because nobody is going to cross a 50 km strait in a canoe/raft/boat with a wild dog.
Presumably they went wild again afterwards, but it must be easier to re-domesticate a dog that was domesticated a few thousand years ago than to domesticate an entirely new species.
Floating there on its own seems pretty unlikely, since Australia didn't acquire any other wildlife from South-East Asia. At the time of British settlement the dingo was the only placental mammal on the continent, apart from bats and humans.
The Australian Kelpie is part dingo part collie (originally). The resulting animal is an extremely intelligent but hardy working dog. One that works all day in hot conditions but follows its master unwaveringly. I would say that Dingoes aren't true wild dogs.