Well, J&T, technically the Caribbean isn't part of the United States of America, just North America!
While an Australian license is adequate for driving on the road, you do need to know the rules of the road wherever you're driving. In the US, ignorance of the law isn't considered an adequate legal defense! Fortunately for you, the laws in most states are similar enough that you don't need to know every last state's picayune differences - pick the one or two states where you plan to do the most driving and obtain a drivers' handbook for those states. Most state DMVs (Department of Motor Vehicles) will distribute them free in person and you can probably access PDFs of them online.
BTW: we don't just drive on the right, we also use the English system on the roads, with speed limits in miles per hours (MPH) instead of km/h. All road signs are in miles as well. Legally, we were supposed to switch to the metric system in the late 1980s but the law signed by President Ford was "conveniently" forgotten due to the cost of the conversion. On the plus side for you, though, is that practically all current-issue cars in the US have sub-markings on the speedometer in km/h, allowing you to use it like a conversion scale.
What exactly did you have in mind for your grand trip, in terms of what you wanted to do, where you wanted to go, what your goal (or lack thereof) may be...? Depending on your destination, it's entirely possible that a car may not even be necessary.