Okay, look. There's no such thing as not having an accent, if you speak a language. In America most people don't consider themselves to be speaking with an accent, because they're surrounded by people with the same accent. But I'm sure, to you, when you watch American television, it sounds like we have an accent. It's the same thing to anyone outside of Australia who listens to an Australian speak. Here's a link to explain.
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The first generation of children will draw on the accents of the adults around them, and will create something new. If people move to a new place in groups (as English speakers did to America, Australia and New Zealand) that group usually brings several different accents with them. The children will draw on the mixture of accents they hear and create their own accent out of what they hear. The modern accents of Australia are more similar to London accents of English than to any other accent from England -- this is probably because the founder generation (in the eighteenth century) had a large component drawn from the poor of London, who were transported to Australia as convicts. The accents of New Zealand are similar to Australian accents because a large proportion of the early English-speaking settlers of New Zealand came from Australia.