Cornell's book cruising routes gives a lot of information on this.
We met a couple of boats in SE-Asia coming from the Med without much trouble. I think there even was a Rally a couple of years ago: www.redsearally.com
The northern Indian Ocean got light winds most of the year due the moussons. That should not really bother you. The same for Singapore southwards. That is, if you take your time and wait for the good seasons.
Darwin and later from the Great Barrier Reef southeastwards brings you in the strong trades; that'll be the hard work I presume. But you can go south inside the reef, that makes the beating upwind much more comfortable and you can wait for favourable weather.