Drago = best answer I've ever seen on Yahoo Answers. Edit: No way, he got dragged!
Yet, the reason you shouldn't say that in Australia is because we do not refer to them as 'shrimp' unless they are smaller than a dime. In Australia that family of crustaceans are called Prawns.
'Barbie' is an accurate Australian shortening of Barbeque but "shrimp" was used in the advertisements instead of 'prawn' as otherwise Americans would have not understood what he meant.
People have warned you not to use the phrase:
a) because 'shrimp' is your word not ours,
b) because it will remind them that on an international stage, Australia is often misrepresented
c) because many foreigners (and especially Americans) attempt to use Australian slang in an attempt to show cultural awareness- yet unfortunately it is often so awkward an attempt it seems like mockery.
d) It makes many Australians angry that stereotypes are all Americans seem to know about our country.
Other things to keep in mind:
Fosters; we export that crap as no one drinks it here.
Koalas; yes they are cute, but they are also surly little bastards who don't appreciate being handled (and as marsupials have zero relation to 'bears' and should not be referred to as that)
Australia is highly diverse, as a continent the size of the US we have a vast range of environments and our people are as diverse as well. It is a young country but highly multicultural, these days even in regional centres.
The majority of Australians are very secular and tend not to be nationalistic yet are very proud of our country, its history, traditions and culture. Most are very open and honest with both the good and the bad of history, but it seems that often the bad is all that makes news overseas possibly because we don't have a culture of talking ourselves up and tend to lampoon tall poppies that do. I'm sure just about anyone will be very willing to discuss any topic or issue you might read or hear about, even those you might feel are sensitive. Just keep in mind how you would broach such topics at home and you should be fine.
Hope you have a great time and get to a barbie or two.