There are in Australia...

"Land Down Under" anyone?
"Waltzing Matilda"....
Country music is also very popular there so you get a lot of artists release patriotic songs about various aspects of Australian culture. Slim Dusty is the one singer who comes to mind the most.
I don't follow country music at all, but I am sure some of the Aussies on here could reference a few examples.
Australians also are proud flag bearers - the boxing kangaroo and national flag tend to be the flags of choice seen at sporting events.

New Zealanders don't really have any patriotic songs.
"Don't Dream It's Over" by Crowded House is NOT considered a patriotic song... nor is that darn Dave Dobbyn Footrot Flats song (despite what some Australians might tell you). However kiwi's are very patriotic when it comes to sports - again though - no real 'songs' that people sing over and over. It is more about the flags - the national flag and the silver fern flag (black flag with a white fern on it).


"He's my best friend, best of all best friends
Do you have a best friend too
It tickles in my tummy
He's so Yummy Yummy
Hey you should get a best friend too" - Toy Box