IF the printer is connected to the desktop, you have all you need already (I am not sure from what I read that it is). It sounds like you already have some kind of network setup. The desktop that is "no longer used" will make a great host or printer server for the printer that you want to make available "wireless".

• From Control Panel on the desktop, go to Printers and Faxes.
• Select the printer that you want to make "wireless" by a single left click.
• Right click, and then left click on "Properties"
• On a popup window, there should be a tab marked "Sharing". Left click on that.
• Left click on the "Share this Printer" option. This makes the printer visible, or available, to other computers on your network.
• Go to your laptop computer and add a printer from the "Printers and Faxes" menu in Control Panel.
• You will have an option to "Browse" for a printer.
• Select "network" printer.
• The desktop's printer should be visible to "Add". 

I have done this several times over the years on my home network with different printers. Ninety percent of the time, you don't even have to load the printer drivers CD into the client computer, as the drivers-printer combination on the host computer are all that is used or needed. It's nice to be able to pull into the yard, click print, and by the time I get inside whatever I need is printed or printing.