You can set up a pen so she can get out of the cage, but won't ruin the carpet. Get some tarps (try a dollar store for some cheap ones) and set them so that they extend past the pen. If you want, you can also use foam puzzle mats to give more cushioning, but still use the tarps underneath. You can put blankets, toys and other stuff in the pen so she has stuff to play with, a food and water dish are good too if the pen is not attached to the cage.
If space is an issue, then don't use the mats. You can then just fold up the tarp and fold the pen away when it is not being used. It is a bit of a pain to set up the pen every time, but sure saves space when the bunny is not using it.
I have found that if the pen is attached to the cage, the rabbits tend to still use the litter box in the cage (if they use the litter box). Even if they are running around in a room and have access to the cage, they tend to use the litter box instead of peeing and pooping all over. If they can't get to their cage, then some might use a litter box if one is provided, but some will just go where ever.