Laminate manufacturers all have their own specific instructions for installation and any deviations could void your warranty so always check these first. Some manufacturers do sell laminate that can be installed over short pile carpet that is less than ¼ inch high and has no pad underneath. However, in general we would advise against laying laminate flooring over carpet for the following reasons:
1) Laminate is designed to slide onto a slick surface such as polyethylene. It may be difficult to lay your laminate flooring with ease on a surface like carpet, which will make it stick.
2) Tiny amounts of moisture resident in a carpet can damage the laminate. The laminate on top will not let the carpet breathe causing trapped moisture build-up and mould on the carpet surface. This will eventually damage the boards beyond repair and produce a horrible fusty smell.
3) There needs to be a ¼ inch gap around the outskirts of the room so you will have to cut your carpet up around the edges anyway.
4) Laminate needs to be lain over a firm flat surface with no bumps or creases or it will buckle and warp in just a few months.
Taking up your old carpet can be very tedious and time consuming but shortcuts are best not taken if you want your laminate floor to look its best and last longest. It is best to lay it with the correct laminate underlay than to take shortcuts that may end up needing correcting in future. For more advice on how to lay laminate contact the manufacturer direct.