Type of camera/lens/accesories : Compact or Mirrorless
Budget : RM2.0k
Your Location : Penang
Preferable brand : Anything as long as its reliable
Type of photography u want to do : Typical landscape for family outing, indoor portraits, MOST IMPORTANT is baby portraits who are moving quite fast indoors.
Any specific models in mind? : Nikon D3100, Nex-3 (18-55mm), Panasonic LX-5, Canon G-12
Any specific features u want? : Very quick continuous shooting for 5 seconds. To capture the baby. Also need 720p movie.

I'm really stuck right now as I'd really prefer a compact camera that can fit in a big side pocket rather than a SLR or like the NEX-3 which both need bags or slings.

So far I've not handled the LX-5 or G-12 yet but from the specs it doesnt seem either can shoot quickly and continuously, for at least 4-5 seconds. Am I right or should I go and try it out myself?

I was in the same situation as you were, ended up with a Sony Nex 3K which is almost to the limit of our budgets. But no regrets so far, its truly a good camera.

If you really don't want to end up changing lens, LX-5 can also do the job. If you want to up the budget then GF1 also can be considered. Personally I didn't buy that purely due to cost.