i know this is an oldish thread but had to add my 2 cents here.
I would think that an undergrad degree from an Ivy League uni would be pretty much the same as an equivalent Australian undergrad degree, is it really worth all the effort to do the same degree in the US. Postgraduate maybe?
from my year's research, undergrad degrees are worth pretty much the same from everywhere. uni names just make them sound cooler, that's all. it's the postgrad that matters.
in terms of money, applications and ease of acceptance, you're better off doing a good undergrad degree in australia then applying to america for postgrad. the best advice i've heard for people who really want to experience 'american college life' is to do a study-abroad program.
there was some mention of using an american degree in australia -- from what i know, it's not worth your money. even if you do go to a high-calibre university (and therefore the education is worth the buckets of money you're forking out for it), there's not much point coming back to australia with it.
although there are many highly-paid career opportunities in australia which could make the american education worth it, you're probably quite as likely to get them with an australian degree, and you could probably do better still in america. the advice given to me was that if i go to america to do my undergrad and postgrad, i might as well stay there to make the most of it.
and for once and for all, if you really want to apply to america, just sit the SATs. like sikhman said, most universities require them, and even if they don't, it could look nice anyway.