Are these 2 machines connected to the Internet through a home router, or do they have their own separate Internet connections?
If the answer is separate Internet connections, then, yes, you can get a wireless NIC for your desktop. They do make USB wireless cards, and in fact, there are some pretty good ones out there. If you do it this way, you would want to set up and "ad hoc" connection. There are tons of how-to's in the Internet.
If you are using a router for both machines to connect to the same Internet connection, then you already have all the hardware you need to share the printer from your desktop. There are also tons of how-to's on the Internet on how to set this up.