Some bunnies do chew on carpet. My two females could have care less about the carpet, but Jack loved to chew on the carpet. Check out the home proofing section for tips. Is the new house brand new? I mean if there was another animal there, there is a possibility that a bunny may mark over any old scent. Keep club soda, and a 50/50 white vinegar and water mix to treat bunny accidents.
Carpets are great though for bunnies as they can run full blast, and do the most incredible binkies!
I do suggest you start small. Don’t give her complete freedom right away. The two females wanted to explore right away, but with Jack it took him two months, and that was with me making him.
If you have a pen, then just make sure to try and keep it arranged inside the same way. Allow more freedom gradually so she understand what is "HER" space and what is the rest of the family’s space – this will help make sure Miah maintains her litterbox habits.