I think what you may want to do first is to determine what image or message you want to convey with the name. Is it quality, price, speed, delivery, convenience, etc.? What consumer segment are you looking to serve: locals, low-income customers, high-income customers, a general mix, etc.? Will the name be used for more than pizza, or only pizza? Do you want an Aussie sounding name or a foreign sounding name to carve out a unique niche? Will the pizza be sold cheap and in volume or will it be gourmet in nature? Will the name lend itself to expansion if you later decide to open other stores in other locations, cities and towns?
Usually the best name is one that is not descriptive of the business (good examples are Dominos, Little Caesars, Papa John's). The weakest mark--the kind that others are likely to use without permission or legal liability--is one that is either generic or highly descriptive (e.g., Bill's Pizza). Trademark laws are governed on a country by country basis, but you might be able to find a trademark that is used in the U.S. but not in Australia. I would stay away from all the names used by big U.S. pizza chains because they usually try to tie up their marks in most countries where they might end up doing business. And they have plenty of money to defend their marks. For you, I think a good starting point is to go online and take a look under "pizza" at an online Yellow pages directory of a major U.S. city, like NYC, to get some ideas. You might find a name used by an individual mom and pop (independent) pizzeria that is unlikely to ever be used by the pizzeria outside of the United States.
Once you find a name you like, or a few possibles, you will perhaps want to get it/them cleared for use before you spend a fortune with all the signs, advertising and promotion materials, menus, box toppers, magnets, business cards, directory listings, web-page designs, etc. You might also find it useful to create a logo to go along with the name you finally decide to use. If you go that route, it should also be cleared for use before you invest too much in it.
Maybe you can create a list of possibles and run them by the members here