The problem is that you need a DHCP server service running on the laptop. I am certain that XP doesn't provide that service. You should just give the Fedora machine a static IP and configure DNS servers as well. If you feel adventuress, you could download a stand alone dhcp server and install it on your laptop, then run it as a service...
Check the ReadMe file and the DualServer.ini file for configuration help. It might be a good idea to check the "ipconfig /all" command on your XP laptop while connected to the internet via dialup, as dns addresses assigned may change frequently...i.e., check to see if the dns addresses stay the same for you. Further, can you actually still connect to the internet with a static IP on your laptop via dial up?
Check the google link too: