Hi,
I'm personally a graduate from UMelb. I would say, go for it! It's not only about what you will you be studying or which university is better (local or overseas), but its more of what you can learn and broaden up your perception. When you actually lived there and experience things, you will definitely think differently and see how a western country actually differs from our usual daily perception.
Singapore to Australia isn't very far as well. Its only a 6.5 hours flight or even 4 hours flight if you chose to study in Perth. Not only so, you will be able to travel around Australia during your breaks with your friends or family.
You will meet all sort of people whom you will never see in Singapore. Now I am back in Singapore to work, I do see that having a reputable overseas degree (ANU, UMelb, USyd, those universities from the group of 8) do help in your job searching. I also realise how graduates from overseas thinks differently from local universities graduates. Furthermore, when you interact with people, you can share your experiences with others which people can feel and differiate yourself from others. So, if you have the opportunity/chance to study overseas, why not! I didn't regret going overseas to study at all!
Give yourself a chance, and it will be an amazing experience.
Good luck!