Wear whatever you are most comfortable in. Remember that the cold European winter isn't anything like the roasting Australian summer you may land in
You are flying in SQ A380 business class. You'll have a huge amount of private space and essentially won't need to make any contact with other passengers. The crew are attentive and if there are any problems, just ask them and they will try to help.
You can pre-book your meals if you want at
www.singaporeair.com - it's called "book the cook" and I'd recommend their steaks
When you arrive in Singapore make sure you go to the SilverKris lounge (which is for business class passengers), not the Krisflyer Gold lounge (for Star Gold customers); the SilverKris lounge is apparently significantly better (I've never been in the Gold one to compare). There are showers etc to use and both times I've visited, with busy lounges, there has been no wait to use showers.
Enjoy your trip