Two main reasons:
1) The Americans were going into Iraq, but not into Zimbabwe. The Brits and certainly not the Australians don't have the kind of manpower to successfully stage an occupation. The Americans do (albeit they've totally ****ed it up in Iraq). And both the UK and Australia are keen to demonstrate that they are good, loyal, friends of the US.
2) Howard, for an absolute fact, believes that terrorists pose a threat to the security of Australia, and also believed at the outset of the Iraq adventure that somehow booting out Saddam would reduce the likelihood of terrorists striking Australia, its interests abroad and the interests of our friends. Now the logic as to how (a) would lead to (b), and whether its had the intended effect is obviously extremely doubtful, but Howard definitely believed that to be the case at the time, and I'd say still believes it to an extent now. From what I've seen Blair is much in the same boat. and the problem is now that the coalition has so thoroughly damaged Iraq now that it could turn into exactly the kind of failed-state, haven for terrorists that used to exist in Afghanistan - so they may have actually created a self-fulfilling prophecy... idiots!
Obviously from that point of view, what happens in Zimbabwe is irrelevant, because no Zimbabweans have flown a plane into a building or blown up a subway.