Hi we recently flew to America with a three year old, I thought it was a good age to fly ( contrast eg with a hideous experience of long haul when she was 11 months).
I took a trunki and bought the bag to go inside it. I went to pound stretcher and bought loads of cheap toys, colouring books, stickers, etc, headphones ( novelty), one of those battery operated fans etc etc... All helped pass the time. Most of the flight she spent watching the cartoons though. Food wise I took a small cool bag full of biscuits, mini breadsticks, sweets etc. have fun!
Hi, I flew to Sydney on my own with my little one and I couldn't have asked for a better journey. I booked the first leg to be during the day and the 14hour leg to be over night. I took his pillow which made it so much easier to get him to sleep, I bought books and puzzles from pound shop and wrapped them up pass the parcel style which took him a while to get into then he had a brand new toy to play with. Also try and book the bulk head seats so you've got that little bit more room. I got lots of stickers for him to decorate his cabin bag (and me) with In between flights. Hope this helps and have a great trip!
Hi Cracker, I've flown to Melbourne quite a few times, as my mum's been out there for 25 years, but only twice with DC, first time DD was 16m (nightmare journey from hell!), most recently a few weeks ago when she was 3.11.
Hopefully Singapore Air, like Emirates, has seat-back TVs with loads of films and programmes and hopefully your DD will kept busy for a while with that! Sticker books are great, and magazines (best to avoid any toys with small bits that will get lost) and we bought some new colouring stuff for DD in a new little pencil case that she hadn't seen before. Hopefully you've requested child meals for your DD, but don't rely on them, as our DD wasn't very impressed and really just wanted snack-type stuff, probably because her body didn't know what time of day it was, so make sure you bring on board the type of snacks that your DD likes.
If any of the flights are night-flights it's a good idea to bring pyjamas and any special bedtime cuddlies to help settle your DD into (hopefully!) having some sleep.
My mum lives an hour or so out of Melbourne near the Mornington Peninsula, and we didn't get into Melbourne itself this time, but there is a decent zoo (can't remember exactly where) and an aquarium in the centre. A ride on a tram would probably be a nice activity. The Southbank area in the centre near the river is nice for a walk, with lots of restaurants etc. If you feel like travelling a couple of hours out of Melbourne the Healesville animal sanctuary is lovely, with lots of native wildlife
Hope some of that is of some help, hopefully there will be more knowledgeable types along on things to do with your DD in Melbourne.