antivirus tips and antivirus download:

Depends how they share it.

. . . With Norton 360/Anti virus/McAfee etc you should be fine. . .

**-Hope it helped-**

It depends on how they share the printer. If it is simply a shared USB connection to a USB hub then you are safe in that respect. The way printer protocols interact over a USB interface would make it very odd to write a virus that would make it over this connection.
However if the share is over the network (wired or wirelessly) a virus can propagate itself through their shared network connection. The printer itself is generally not the weak link (although some newer and fancier ones do have built in web servers that if left configured to default settings can help the spread of malware). Whenever you connect any machine to another that is connected to the internet you accept some amount of risk of compromise. This is why big corporations have network areas called demilitarized zones (DMZs) that are away from their local intranet and are connected to the Internet.
Even if they are not directly sharing a network connection, you yourself could spread infections with things like a corrupted pendrives/flashdrives or a compromised file that contains malware hidden in it. It is common for bad viruses to spread themselves to connected media in hopes of infecting other machines.
In the end it is always important to practice safe security measures: encrypt your important information and back it up regularly. Do not rely in things like Windows internal “restore points” because those can easily be corrupted or plagued with viruses nowadays, but rather run backups onto an external drive to an encrypted container. If a file looks new and strange, do not mess with it. Etc.

Yes, your computers share the printer through a gateway. So if the PC online gets infected it can spread however, if you configure the firewall on the work PC to only allow printer related packets to come to the PC, then the chances of getting a virus are trimmed way down.

Basically, the more access the computer connected to the internet has to the work computer, the more chances a virus can spread. And by access i mean what is allowed to come through, even though you might not know it.