Ok, first thing I notice is that you are using a old(er) version of avast.
Latest version is 2015.10.2.2217

If I understand it correctly the printer is physically (through a usb/parallel cable) connected to Desktop.
How is the laptop connected to it ?

Are you using internet connection sharing through the desktop ?
Are you using a router ?
Are the systems both directly connected to a router / modem ?