I would at least leave it till Christmas - your DD1 has just left school, where she may have been with people for many years (in my case, there were a handful I'd known since pre-school playschool.) Going to university is very exciting, but it's also quite daunting, and her room may currently feel like it's the only thing she's really in control of and gives her a sense of continuity. By Christmas, she'll have had a term to settle in, will have a better idea of what stuff she really does or doesn't need, and will have had a term to think about not being at home and being in a new stage of life, and will probably be more amenable to swapping rooms.
It also sounds like the idea of swapping rooms has only just come up - unlike people who have been talking about it on and off for years. She'll need time to get used to the idea of it, so she doesn't just feel pushed out and rejected. My mother always made it clear that we were expected to leave home once we got to 18, so it wasn't really a shock when my room turned into a guest room, but it still felt a bit like I was being pushed out, because it put me in the same category as extended family and friends, rather than their daughter.
My younger sister never wanted my room anyway, as she always had the bigger, better room, but it was always the rule that if we had guests over, they got my room, and I would have to share with my sister in her room for the duration. (Didn't stop us complaining, to be fair, but we did know we wouldn't be able to overrule it.)