I believe you need to set up your Fedora to perform IP masquerading. This is where any requests from the internal network (in your case, the laptop), are mangled so that they appear to the outside world to be originating from your gateway machine (the desktop).
There are two programs that I can think of that will help you get this working:
Guarddog - This is an easy to use GUI for configuring a firewall on a Linux box.
Guidedog - This is another program, designed for use with Guarddog, that can configure your machine for IP masquerading (i.e. act as a gateway for you laptop).
Hope this helps.