If you have a rabbit and carpeting then you probably have a rabbit that digs in that carpeting. Digging is a very common behavior because it is also a very natural behavior for rabbits. In order to keep house rabbits from digging up your carpet and doing other destructive behaviors, you will need to give your rabbit something that is okay for her to dig (an alternative to carpet) and teach your rabbit what is off-limits.
Provide Your Rabbit With Alternatives to Carpet
Since your rabbit has a natural urge to dig make sure you provide something in which your rabbit is freely allowed to dig. Make your rabbit a digging box out of a large, fairly deep cardboard box (cut one side lower or make a hole to allow your rabbit to get into the box). Then add a thick layer of shredded paper, hay, or even chemical-free soil (this option will be messy though) in the box for digging. You can even hide a couple of toys or treats in the box for added interest. Smaller boxes or litter pans with shredded paper or hay can also be offered for additional digging opportunities. Untreated grass and sisal mats (these can be purchased in the pet store) are also great for satisfying your rabbit's urge to dig.
Rabbit-Proof Your Home
Protect places in your home where your rabbit likes to dig (wall corners and under doors seem to be attractive digging spots for many rabbits).
You can put down plexiglass, plastic floor mats (like those for under office chairs), linoleum, floor tiles, heavy mats (like entrance mats), grass mats, or move furniture to cover or block areas your rabbit favors. If your rabbit wants to dig your furniture, cover it with heavy throws or blankets to protect it.
Don't give your rabbit free run of your home at first until your rabbit is trained to not dig where he isn't allowed. Pick a limited area for your rabbit and thoroughly rabbit-proof that space to make training easier for you both.
Supervise and Redirect Your Rabbit's Behaviors
Your rabbit doesn't instinctively know that they are not allowed to dig on your floor or furniture so you must teach them. When you are starting out with a new rabbit, watch your rabbit carefully at playtime. Make sure you start this training as soon as you bring your rabbit home so no bad habits start early on. Whenever your rabbit tries to dig where they should not say "no" firmly but calmly, clap your hands (or stomp your foot on the ground) to get your bunny's attention, and then take your rabbit to their digging box to encourage the digging behavior in the appropriate place.
Have Patience With Your Rabbit
It will take time for your message to sink into your rabbit so be patient but consistent. Never hit your rabbit under any circumstance. If your rabbit keeps going back to your things instead of digging in her box, put them in a "time-out" in their cage for a few minutes. Another alternative is to use an exercise pen (they make them for rabbits and pocket pets) placed on a sheet of linoleum to protect your floor during at least part of the playtime outside of the cage.
As your rabbit gets older and settles down digging should become less of an issue and you should be able to trust rabbit more.