I promise this is a dog training question...

I’ve had an indoor (neutered male) rabbit for about five years (I believe he was a few months old when given to me). In the past year he has started chewing large holes in the carpet. Not only is it unsightly but I can’t find anywhere that he’s using the fibers for a nest so I believe he is eating it which I imagine is probably dangerous for him. The only way to prevent it I know of would be to lock him in a cage but I don't want to make him live that way after having free run of the entire house all his life.

I also have a Blue Healer / Lab mix. She chases the rabbit playfully. Sometimes when she's napping if the rabbit feels like playing he'll nudge her until she wakes up and runs after him. I've built a partition on a window seat where he can jump up and escape her reach if he wants to end the game. This has essentially become his hutch (but it is never closed or locked).

Now... If I could figure out how to train this half-breed livestock dog to herd the rabbit to his hutch whenever she heard him tearing up the carpet (which is actually quite loud) the problem might be solved.

Does anyone know how to train the dog to police the rabbit this way if it is possible to do?

TLDR:
-How do I train a livestock dog to herd a rabbit?
-How do I train her to perform that task cued by a sound the rabbit makes rather than a command from me?