If you don't want to wait there is actually a way to restore a 9.1 backup to a 9.0 device. Since the difference between 9.0 and 9.1 is so small (effectively no new settings or anything) it's rather unlikely for there to be issues.
WHat you need to do is:
1. Backup your old device to iTunes.
2. Go to where the backups are stored, on Windows this is in %AppData%\Apple Computer\MobileSync\Backup\791cdf4e127a627ba0113533e07f5c6c488038da on OS X I think it is in ~/Library/Application Support/MobileSync/Backup
3. Find the backup that belongs to your old device, if you just synced it'll be the newset one, look at the create times
4. Open the backup directory and find info.plist, open it and search for 9.1, when found, replace it with 9.0 and save
5. Restart iTunes and it'll now let you restore this backup to your new device even though it runs an older OS version.
Make sure you have the latest version of iTunes, I hadn't updated and with the last version it had touble syncing over all the apps, just stopped for some reason and unplugging and plygging in again caused iOS to forget the not yet synced apps and their data. With 12.3 all apps and their data synced over correctly in one go.
Also had an issue with it asking me to sign in to iTunes Store but verification would fail because of "Unknown Error", this cleared after I canceled it (several times) and got through the initial setup, maybe the iCloud login at the last step fixed it. Went back and did pass code and TouchID after that.
Apart from those two issues it worked for me. If you don't want to wait it doesn't hurt to try it, should there be an issue you can always reset and wait.