A Jacobs Ladder produces enough current at a very high voltage to draw an arc that will grow up the ladder to an inch (~25mm) or more. That's very likely to kill a chicken or cat. Don't use that for an electric fence.
Most electric fences are powered by a circuit that generates a short high voltage pulse at a low current. They're not normally deadly to livestock or small animals. You are far better off looking for a circuit purpose built for use with an electric fence.
An experimenter kit that I used many years ago used an audio transformer, similar to those used in transistor radios, together with an oscillator that would output a pulse a few times each second. It was not deadly but would give a good sting to anyone touching the two leads. That's a far better route to take for an electric fence.