Apart from the question if websites could access your printer settings (which is a very interesting one that should definitely be answered by someone knowledgeable), I would always recommend two things:
- Deny access from VMs that can access the Internet to your local network and vice versa (using Qubes firewall settings or, if possible, even dedicated network VMs)
- Put your printer settings in a dedicated disposableVM (see, e.g., "Now You're Thinking with Qubes" - #5 by phl)
Both help with stronger isolation of your digital life in general. If you would want to print something from the Internet you would then:
- Print page to PDF in (tor)browser
- Navigate to PDF in file system
- Right click → View in DispVM (which would open a disposable PDF reader with access to your local printer)
- Use the regular print menu from there.
Just make sure you leave the dispVM open long enough for the printjob to be fully transmitted. Especially with larger files, I sometimes close the window before all data has been transmitted to the printer and then the job aborts.