As Nigel says.
The pet tags apparently operate on 134KHz and although its "radio frequency", the function is more like transformer coupling between the coil in the reader and the coil in the tag.
The operating range is pretty much dependant on the size of the reader coil, within reason.
It may be possible to get to a foot or two, with a coil on the reader two or three feet diameter.
Just for context, a conventional "half wavelength" dipole antenna element would be roughly three quarters of a mile long at that low a frequency, vs. about 5ft for FM radio or something like a foot down to eight inches or so for the higher TV frequencies.
edit - typo