Omit Ethernet Card?

I am about to start setting up my home wireless network.  My primary interest in having the network is being able to only access the internet with my laptop.  I don't plan to share information or access any files located in my desktop.

My question is:  Can I eliminate the use of a netwok adapter in my desktop?  The ethernet cable plugged into my desk top ethernet card will be plugged into one of the four ports in my router.  My laptop has a built in network card so I an thinking that since I am only interested in accessing the internet why have the network card in my desk top?

Hope I have made this clear for someone to offer some advice.