Don’t get the new carpet!!!
My advice would be to start moving the litter box now, before the flooring gets done. It might also be handy to add an additional one in the new location, put hay in it etc, and day by day start moving the old litter box closer to it (might only be a few inches or a couple feet at a time). Your rabbit may just start using the new litter box on her own just because it’s there. You can help the process by scooping some dirty litter into it as well. You should be able to transition her fairly easily to using the new location if you allow the time for it.
My main concern is blocking her off from the places she’s used to going. She will not be happy about it, although I certainly understand the need for protecting carpet from enthusiastic bunnies. How are you planning on keeping her from the carpeted areas? Baby gates or something else? She will be frustrated about not getting to go in those areas so whatever you use to block her needs to be very secure, or she will work at the weaknesses until she figures out how to get through
She won’t be traumatised, but be prepared for some bunny tantrums.