Well, not really.
See, this is one of those really weird things in Australia. The Queen of England is also the Queen of Australia, so it's fairly logical to celebrate her birthday since she's, you know, Queen. Which - by the way - is 21 April.
However, every state (with the exception of Perth and the rest of Western Australia) observes the Queen's Birthday on the second Monday in June.
Why? I don't know and most Aussies probably don't either.
But hey! Any excuse to kick back and enjoy a stubbie is good enough for everyone.