A ‘new’ Scotland would have kept the Queen. The RF is Scottish after all (despite most people thinking they are English or German).
That is a debate that will not be waged....the House of Stuart would disagree about who would be Queen:
http://www.express.co.uk/news/uk/460698/House-of-Stuart-s-Duchess-of-Alba-could-be-next-Queen-of-Scotland-after-independence-vote