Use your N810 with MaemoMapper to either connect to a KISS TNC and 2m radio or to the APRS-IS internet feed.

Equip your cat with one of the all-in-one APRS trackers (www.byonics.com) with radio, GPS, tracker, and battery.

Your N810 will update with the location of the second device as it beacons it's position, in real time.

Just need your Ham license.