First, one would have to define the "survival" goal. What is supposed to survive? Most of the population? A viable industrial base? A sovereign nation? A distinctive culture?
Consider a Preemptive Strike
If the decisionmakers are certain that the Soviets will deliberately (or accidentally) start a war, most of the arguments against a preemptive strike will be gone. Sure, there will be megadeaths. Sure, there will be nuclear winter. But the best way to ride it out is to have your forces start a deliberate, well-rehearsed attack "out of the blue" to catch at least some of the enemy force before it can be launched.
Identify what you need to rebuild an industrial base and put it into distributed shelters. Machine tools. Generators. Refineries. Drill rigs. (Of course the plans will fall short. For want of a nail it will fail.)
Build shelters for the population and equip them to dig themselves out of the rubble and to travel through contaminated zones to a place of safety. The US is large enough, especially in cooperation with Canada and Mexico, that there will be some "less contaminated" areas where people can try to survive. Sure, cancer rates will rise a lot.
If the survivors had the ships to travel to Australia, would the Australians welcome them? And would the result be "USA Reborn" or "Unemployed Refugees Down Under"? The outcome will be better if it was prepared by secret negotiations and if the refugees can bring the contents of Fort Knox, plus machine tools etc.
Of course if the plan got known, Australia might get plastered, too. So talk with South Africa. Argentina. If nothing else, rumors of these talks would force the Soviets to spend nukes on empty desert. Reduces the rad count in Kansas.
Follow-Up: Balance of Forces
In the early 60s, the USSR had only a few intercontinental missiles. Their other missiles and bombers didn't have a truly global reach. Understanding the truth about the "missile gap" might make all three options more palatable. The President and his advisors might even see a limited window of opportunity to do so, and decide to act now to save at least some of America. They might argue "fight now, and when the dust settles 100 million Americans will be left. Fight in five years, and it might be none."
Mao is said to have dismissed megadeaths that way. Don't count the deaths, count who will have more people left. Might have been bluster, might have been cold-blooded calculation.