There's nut-server project to take care of the shutdowns. Compatible UPS can be read from using SNMP or USB and nut-server can distribute the status to the clients. Clients may elect to shut down.

Does your desktop actually drain 1kw during normal operation? If so, yeah, it would probably benefit from a separate UPS. You might not need to replace the whole thing though, just the batteries -- admittedly they are the bulk of the cost.

WRT cats -- I got myself a network cabinet for precisely that reason. Also minimizes the amount of fur getting trapped in vents.