The term "Australasian hamburger" typically refers to a hamburger that has been topped with beetroot, pineapple, and a fried egg. If you're looking for synonyms for this particular type of burger, you could refer to it as a "kiwi burger" (given that the ingredients are popular in New Zealand cuisine) or a "down under burger" (given that the ingredients are typically associated with Australia and New Zealand). Alternatively, you could refer to the burger by its individual components, such as a "pineapple and beetroot burger" or an "egg-topped burger." Whatever you choose to call it, this unique combination of flavors is sure to satisfy any hungry appetite!