New iTunes account and apps?

I want to make my daughter her own iTunes account. When I do, I imagine her apps will disappear when she syncs her iphone, right? My question is, when she downloads the apps again into her new account, will all her progress in games come with it since the app was already on the device? I believe the game saves are not associated with the iTunes account, but rather on the phone itself or iCloud.

If you authorize the computer to HER itunes account, every time she plugs in her iPod, It will ask her if she wants to restore and sync the apps. DO NOT CLICK YES! Just ignore this warning when it pops and all shall be good.