Wireless router is what you are after, cheap and easy (like all the best things in life)
some wirless routers (of a decent quality) will have ethernet out aswell as in, so you take ethernet in, broadcast to the lappy, and then back out to the desktop (thats what i do anyway) your method would require that you leave your desktop on the whole time.
the other option is that your broadband modem might have two outs, or of course replace the modem with a wireless route / modem like the home hub
Or use the dongle method above
Agreed, no point having more equipment than is necessary. A single wireless router like the Linksys will do the job just fine