The new ‘Device Transfer’ feature in v.1.2 allows you to do this. You retain your user name, character, wardrobe and all of your points. The only catch is that the instrument packs you’re using are not transferable – you will need to download them again on your new device (and you won’t have to pay for this if it’s the same AppleID). So although you will lose your practice statistics and homework history, you won’t lose your place on the ScaleBlitzer leaderboard!
To transfer your character and points to another device, select the ‘Transfer Character’ button in the Character Options screen. You’ll get a message warning you that your character is about to be transferred (it goes up into the cloud). Once you say ok, you simply log in on any other device that has ScaleBlitzer. You can also bring your character back to the original device! (If you do this you’ll come back to all your packs and practice stats.)