Every computer, including the XP machine should have its own anti-virus and malware protection. Don't rely on Windows Defender (or the older Microsoft Security Essentials) they offer far inferior protection compared with Kaspersky, Norton or Avast.
There are still some reliable AV packages that work with XP.
Much of the scaremongering about XP being unsafe because Microsoft are no longer offering security updates refer to the computer being hacked rather than getting viruses or malware. Since you mention a home network and other machines, that implies a NAT router. The NAT function and the router's firewall provide a high level of protection from hacking except if a machine is in a DMZ, or you have configured port forwarding to a server on a machine with an insecure server App. In the latter case, it is the App creators responsibility, not Microsoft's, to fix any security bugs. Such bugs could potentially affect any machine on which the App is installed, not just XP and now Vista systems.
I still run an XP netbook without any problems. I use it when on holiday as an entertainment machine with various films and music files installed on D:, which is also where I backup digital photos from my cameras until I get home. I have a DVD with the computer that contains a full image backup of C:, less the latest AV signature files. Since I do not add any new Apps, then I only need to create a new DVD every year or so. If the films or music get damaged, I can restore then from my main backup HDDs when I am next home. A couple of weeks having to rely on TV, if the netbook loses its entertainment files, is not a major issue.
I hope this helps.