My bunny did the same thing. This was a huge frustration among other naughty things she would do as well (I was on the verge of tears because I felt so bad for having to keep her kenneled and was not expecting to have such a naughty bunny all the time). What worked for me was I spent a weekend sitting on the floor while she had play time – and every time she would try to dig or eat at the carpet, I would clap my hands and say NO – in the kennel you go. I would then nudge her to the kennel and lock her up for 10-15 min. Once she was let out she would return to the same place and do it again. I would repeat the clapping of hands and No and having her back in the kennel for 10-15 min. This went on all day (she is very persistent). The next day she would do it but when I would clap my hands and say no – she would stop on her own, but I still had her kenneled after each attempt. I have found that rabbits are very smart but also very stubborn. I also had to block her from going under the furniture I did this by placing 2×4 under the furniture so she couldn’t even get her head under. Thankfully home depot will cut the wood to size for you.
I can say, that until I got her spayed her bad behavior was constant as I spent many hours to get her to stop doing the naughty things only to have her training only last a week or so. Once I had her spayed about 2 months ago she has really settled and is becoming a wonderful bunny. She is able to be out of her kennel for hours at a time again with only me having to say no and clap my hands once or twice during the day and she knows when she is naughty – I will say No and she will run back to her kennel on her own (of course she then acts like she is mad at me and pouts in the corner). Spaying was not cheap it cost me 350.00 but was well worth the money.
Also, I have found that if I keep her nails trimmed she is less likely to want to dig at the carpet.