I booked through Trailfinders but I don't think it really matters, go with whoever you get the best deal with.
We stopped over in HK, but Singapore is nice, friends stopped in Malaysia and enjoyed it.
Don't know about weather at that time, variable I've heard.
Lots to do there - if you want to see Aussie animals Healesville Sactuary is great (miles away so need a car). We went to St Kilda, to Luna Park, that was fun. But we had the kids with us.
It's a really nice city, you'll have a great time whatever you do!