You have two options.
1: Install 9.1 on your new 6s before restoring from backup.
2: Revert your current phone down to 9.0 just before getting your new one and make a 9.0 backup. (Reverting is easy. Download the .ispw file for 9.0 then in option + clicking update button in iTunes. It won't even need to use a backup, it literally keeps everything and just changes the iOS version.)