Barbie is simply a shortened version of barbecue. An iconic Australian phrase you hear around is "shrimp on the barbie" originated in a TV commercial series by the Australian Tourism Commission starring Paul Hogan in the late 1980s. Australians, however, more commonly use the word "prawn" rather than "shrimp". Because the commercial was commissioned for broadcast in the United States, the change was made to limit audience confusion.
Have a Captain Cook is an Australian rhyming slang term to Have A Look. They say Captain James Cook "discovered" Australia back in the late 1700s.
Chippy comes from the reference to the wood chips that fly as Carpenters work their magic. Other Tradies (Tradespeople) are referred to as Brickies (Bricklayers), Sparkies (Electricians), Garbos (Garbage collectors) and Cabbies (Taxi Cab drivers).
Dog's Eye is an Australian rhyming slang term for Meat Pie – an Australian cuisine consisting of buttery pastry surrounding gracy and mince meat of varying quality. Often served with tomato sauce and mushy peas.
Dunny can now be used for any toilet. The word comes from British dialect dunnekin meaning an 'earth closet, (outside) privy' from dung + ken 'house'. First recorded in the 1930s but dunnekin is attested in Australian sources from the 1840s.
Servo is short for "service station" and the the "o" is added to give it an Aussie vibe. There are hundreds of examples where we add the "o" and here are a few iconic and common examples: Defo (definitely), Muso (musician), Vego (vegetarian), Aggro (aggressive), Tommo (the name Tom), Jono (the name John) and Arvo (afternoon).