I finally got her a pair of proper scissors. Unfortunately, I couldn't get the pair I saw at Borders which claims that the blades of the scissors will not cut skin so I had to settle for another pair... and well, I decided on getting Crayola's. It costs no more than $4, comes in a few different colours and it's good for both righties and lefties. It's got a blunt tip but no promises that it won't cut skin... :P
Alicia's not very good at the cutting as she lacks strength to move the blades of the scissors continuously - the prerequisite of smooth cutting. What she does is pull 'open' the scissors with both hands and then get her the scissors in the right position for making a cut with her right hand.
Remember to supervise your little one closely when she's using the scissors! :P