I spent a month in Malaysia a couple of years ago and found it very easy to eat with rice, veggies and fresh fruit galore! KL particularly has some awesome options! It has my favorite Indian restaurant in the world, Sri Nirwana, which at the time at least, had plenty of vegan options:
http://www.kuala-lumpur.ws/food-dining/ ... .htm#promo. It's in the Bangsar Village, which was an easy cab ride from the airport.
It wasn't super easy to avoid oil, but some places offered steamed rice and veggies and curries and that was a lifesaver!
Best of luck!