Well, this is an interesting question. The laptop is not radioactive. It doesn't 'irradiate' anything but heat. HOWEVER, the transceiver for your wireless connection does put out a tiny bit of microwave radiation - just like a cell phone and, to most people's surprise, that microwave radiation is just the right frequency to soak into your soft tissue. Particularly your brain. Microwave radiation loves brains. Odd, but true. Well, in a everyman scientist sort of way.
Many folks, health care professionals, believe that for some susceptible people (who can't be id'd beforehand) that microwave cell phone radiation will contribute to the development of brain cancer after long term skin to phone exposure.
The epidemic of brain tumors (particularly in men) that began about the same year cell phones became widely available and moves roughly in concert with the growth of cell phones is evidence enough. But, the vast majority of people could use a cell phone their lifetime and never have an issue. Some sort of genetic predisposition is in play but we probably won't know about it for 50 years.
Now, reproductive tissue sort of likes microwave radiation too, but I don't suppose you've got your wireless antennae too close, no? Even if it's six inches from your lap you're getting a dose that fades dramatically with distance. You probably have absolutely nothing to worry about. Probably one cross country airplane flight would give you 100x the radiation uptake of a lifetime of spending evenings with your wireless connection on your laptop. Just to get all Carl Sagan on you.
But, she's not entirely wrong. Freakish, isn't it?