I light it according to the instructions, turn the dial from Pilot to On, and within 20 Seconds the pilot goes out. I can hear the wosh noise (stop laughing), and then it goes out.

You need a new thermocouple. You can get a kit at almost any building supply or hardware store. Also, at an HVAC supply store you can find them. When you replace it make sure that only the 3/8" on tip is in the flame.