I assume that both computers are running Linux. Then you can configure cups on your downstairs computer to publish the connected printer. The cups daemon on you upstairs computer then automatically sees the published printer and you can select it from the usual printer dialog.
You can configure cups via the web-interace, i.e. you can connect to http://127.0.0.1:631 (on the computer with the printer.
The automatically discovering of the shared printer on the printer-less computer only works, if both computers are on the same subnet and if the computer has the show-broadcasted-printers-option in cups enabled. Don't remember what is the current default under Ubuntu.