It could be a problem since laminate floats on the supporting floor and you will be changing the direction of the pattern unless you cut small pieces-not recommended. If you want to continue, the easiest way is to glue down the laminate and then have the carpet fitted. Is it a slab or wood floor?

I agree. You could cut your old carpet to the size you want and make it into a rug, cover the whole floor with laminate and drop the rug on top. What holds your current carpet in pkace, tackless stripping?