Hello Anna Maria
Firstly I hope you have a wonderful time in Australia and Singapore. Arriving and leaving from Perth is a good start as its so much shorter a flight than from the east coast cities.
Stopping over on the way is fantastic as you will arrive in Australia much more in tune with local time. Personally, I always set my watch to local time in my destination as soon as I get on the plane. I then act as if I were at that time, giving my body as much time to get used to my destination as possible. Eat and sleep as if you were at your destination, and when you arrive, keep going no matter how tired you feel. It will make a difference, I promise ! Leaving on the 11.15 to Singapore you are going to arrive at 7.15 or so I would guess? Make sure you sleep loads on the flight after you have eaten, you might not feel like it but if you can help your body feel you are overnighting you will feel fit for the day when you arrive in Singapore.
Singapore to Australia is only 5 hours so thats an easy hop, and the time difference is only a few hours.
Have a great time down under!
hamsco