Honest opinion, it wont be a case of you say jump, we say how high. Not that it was, but the 2 country's interests are closely enough entwined that thhey should work together on pretty much everything imo.
Rudd pulling troops from iraq is more a silly gesture to get the vote from the anti-war crowd. like i said, he's leaving behind all the logistical troops and platforms, plus a 'security detachment' so in my mind he's not pulling out all the combat troops anyway. besides, he'll send em straight to Afghanistan which is a fight he approves of.
Trade-wise, id expect things to be a little frostier. Rudd is keen to get
very chummy with China, and for that matter the rest of Asia. Unfortunately for the US, that means a bit of a clash of heads. While the US might say publicly that it wants china's growth to continue, ultimately this isnt a good thing for the US. Rudd is going to be actively helping the Chinese economy grow wherever he can, in the belief that this will impress our asian neighbours. this, coupled with similar ideas for places such as Malaysia, Thailand, indeed most of SE asia, will drop the economic relevence of the US somewhat as these smaller economies grow, and in China's case, almost set the benchmark.
Defence-wise, I expect a little less support to go to the US in general. Working 'too closely' with the US led to the perception that Oz is nothing more than a US vassal. To make inroads into Asia, this image has to be shed. A significant part of this will mean defence ties wont be quite as close. Think pre-01 and i think you'll be close. things were tight then, but not living in each others laps.
What will be interesting is that Rudd refusing to sell uranium to India means they're going to have us in their bad books at a time when the US is trying to groom India as a strategic partner for the next 20 or 30 years. If our ties with china become closer, this will make for an interesting strategic environment, as India and China are likely to become regional rivals - one one hand you have the US, India and even Russia, on the other you've got China and Oz - and then, Oz and the US.
I didnt realise this was getting so long, so to sum it up i think the relations between the US and Australia will cool slightly, we'll be at loggerheads on a lot of things that weren't an issue for the past 10 years, but i think on many things very little will change - we've had close ties groomed over the past 60 years, it'll take more than a change in govt to dimish them significantly.