What does the rabbit need to appear to be doing? Can you give a context for its use? Is it about to be crushed, like in Mice and Men, or is it going down a a big hole, like in Alice in Wonderland?
Context means a lot to getting the sense of the rabbit over to the audience. The simplest electronic method of simulating movement would be a battery, a small DC motor, and some sort of cam attached to the motor shaft. You'd put all that inside your stuff rabbit, and make it squirm around. If you wanted an actor to "kill the wabbit," as a certain bald hunter is famous for saying, you could easily add a push-button switch to the circuit mentioned above.