Midvalley Megamall has a lot of local Malaysian trinkets, designers and FOOD!!!!!!! Check out the basement level in particular for the food. It is also connected by walkway to The Gardens shopping, which is one of the luxe malls but also has some food and some stalls with Malaysian gifts eg. local soaps and oils.
Don't know much about Malaysian designers for fashion sadly, but will be following this thread for recommendations, too. It always just awes me so much when I land in Asia and see the enormous explosion of local designers and creativity around.
Singaporean fashion labels I know of include Our Second Nature, Love Bonito, Ong Shunmugam, Shanghai Tang (is that Singaporean?). There are many more. Taka is awesome to visit. G2000 is in both Singapore and KL for affordable workwear/day to night wear.
Have a great trip!