Well, if you think that all of the Nevada Nuclear Tests couldn't even crack one single state apart, the magnitude of power necessary to split a continent like Australia would, well...literally fill the skies with ashes, cause earthquake and tsunamis the likes of which were never seen -in fact, splitting apart a continent would be tantamount to open the planet in that point, the consequences would be catastrophic as to cause total extinction. Not to mention that you need an amount of power that should surpass of several orders of magnitude that it caused the Chicxulub crater -and that in turn surpassed many times the totality of nuclear weapons on Earth during cold war. You do need a whole new technology to do that, or an unlimited budget on nuclear weapons and a will to use them all 24/7 till desired effect is reached.
And even then, you wouldn't change their location, only their structure. Continental drift is caused by the convention movements of magma under the crust no military technology can replicate that. And, to be precise, said underground movement causes drifts and subductions in the crust -and in turn it is this activity that changes the shape and moves continents. If a God tried and just pull/push a continent, the tectonic placque would just bang against another without any other effect -well, save for the mothers of all earthquakes, that is...