I was reading a great book called On the Beach by Nevil Schute where nuclear war escalated between the superpowers but Australia was not directly attacked.
Do we know if the Soviets had plans to attack Australia or would it have been logistically too complicated or otherwise unnecessary?
Similar question about South America as well- I was thinking if some bigger countries managed to escape the inferno, would they become the new superpowers?
We can't possibly speculate on who would become a new superpower after a nuclear exchange — that is hypothetical history, not actual history.
As for Australia — once the Soviets had second-generation ICBMs (late 1960s) or first-generation submarine-launched ballistic missiles (early 1960s), they could have, if they wanted to, target countries in the southern hemisphere. (Their first generation of ICBMs could not, and their bombers probably could not expect to arrive in one piece.)
As for whether they would, I know of no doctrinal document that implies they actively targeted Australian sites or cities. We don't have any evidence of the US storing nuclear weapons at Australian sites (though there are still uncertainties about which countries hosted, knowingly or not, overseas nukes), and while the US did have military bases in Australia, because of its not-really-on-the-way-to-the-USSR-or-China status, I don't think any of them were the kinds of places that would be very attractive targets. (We can contrast this with, say, the air bases in Japan, most of which did not store nuclear weapons, but many of which would have played a supporting role in a US bomber attack, providing refueling and fighter capabilities, and thus would probably have been fair game in a counterforce targeting scenario.)
The Soviets were not in a state of "nuclear plenty" until the 1970s, in the sense that they had a relatively small number of total targeting warheads compared to the USA, which means that targeting US silos and sites would soak up much of their existing stockpile, if they were aiming to be even a little counterforce (that is, using their nukes to target other nukes, with the hope that they might stave off some of the attack). So I doubt they would "waste" any by targeting Australia, who would not come into play in the exchange.
But we don't have a clear cut sense of much of Soviet doctrine from this period, so I'm not sure it is something one can say with much certainty. But I doubt they targeted Australia. It would not have been logistically impossible, but its distance would mean it would have to be very deliberate, something done for a good reason, and I don't think there are adequate reasons. Australia would not pose a direct threat to the USSR in a nuclear war, nor even an immediate one in a post-nuclear scenario.
Assessments made during the Cold War by the Office of National Assessments suggest that Australian cities would have been regarded by the Soviets as low priority as they posed virtually no strategic threat to the USSR. The only sites the ONA deemed as likely targets were the US-Australia Naval Communications Station in Western Australia and the Pine Gap facility. In the event these ere to be destroyed by nuclear weapons, it was deemed that Australia would not suffer much in the way of nuclear fallout not would the destruction of the Northern Hemisphere result in Australia eventually becoming irradiated like it is depicted in On the Beach.
Follow up questions, were there any known targets in American Allied countries, such as Canada or Great Britain as well?