No, don't disable sharing.
In your first post you mentioned "wireless network". This led me to think you have a wireless printer. You might not.
If the printer in question is not wireless, and is only connected to your desktop PC by USB then the behavior you are experiencing is "normal". The Desktop must be on in order to access and use the printer through it. This applies even if the laptop's connection to the desktop is wireless.
You must have a wireless printer to be able to access it independently on your laptop. The wireless printer would be connected to your home network through your router and then accessible by any computer connected to the network that has the wireless drivers
installed. (If the printer has an Ethernet jack then there are other options, but that is another story entirely.)
So: Wired USB printer connected to the desktop connected to the network = desktop must be on or no access, and that is normal.
Hope that helps!