The read range on the 1024 caps out at around 10cm with the largest tags, and that's assuming the tag is held directly above and parallel to the reader. Deviation side to side and rotation of the tag from this position will reduce the range, and smaller tags have a shorter read distance. I doubt the 1024 would work for this solution. The read distance is a limitation of the antenna size and frequency. The 1024 uses "low frequency" communication- 125Hz. You will need to look into higher frequency readers or ones with larger antennas. You'll also need to make sure your pet's tag is compatible with the reader you select. Maybe if the animals are trained they can be shown they need to rub their head close to the reader so the tag comes within range?
Maybe if the cats have significantly different colors you could use a visual solution, like a small camera with frames processed using a library like openCV. Although it wouldn't work well at night then.
