Put your contacts on iCloud or save your contacts to your address book on your computer. Once you get your phone, sync to those but don't restore from backup.
Personally I'd recommend using PhoneCopy (free) from the App Store to back up your contacts on a remote server. Then restore and update to iOS 6 then reinstall PhoneCopy and load your contacts back on That's my personal preference anyway, I'm sure there are various methods other people prefer.