Can anyone offer a solution for a 134.2 kHz stick antenna?

... http://en.wikipedia.org/wiki/Longwave

You missed the critical bit: It may be used for radio wavelengths... low frequency (LF, 30–300 kHz).

Here's a link to a Texas Instruments pdf that describes a 134.2 kHz RFID reader that uses a ferrite stick antenna.

 

This is a better reference: Series 2000 LF Antenna Design Guide - TI E2E

I'm still not clear how to get 580 mH in a stick reader for the SL-134.2 kHz module. I'd like to clarify the specs for the ferrite rod and copper wire size, length and number of coils.

 

A nice Coil Inductance Calculator. I intended to add these quotes from the above guide highlighting the art in antenna design:

Ferrite cored antennas, like... stick antennas... provide a strong localized RF field and perform well in noisy environments. They are easy to construct but do need the correct grade of ferrite for the core...

Note: Because of the different characteristics of various wire types, some experience with this program is required. By modelling and then constructing different sized loops, you can determine what offsets are required for the wire you are using, to get the exact inductance

As a guide I'm thinking an antenna about 300mm long to fit within a 600mm x 25mm PVC pipe (could go to 900mm). I'd want to maintain reading a 30mm ear tag distance of about 36cm.