If your Windows 7 pro is a retail copy, you can also simply do an Anytime Upgrade on your Home premium computer, using the Pro key. Keys are not architecture specific (i.e. whether 32 bit or 64 bit). Heres a tutorial. Guide Windows Anytime Upgrade
Please first make recovery dvds on the home premium computer or save a system image using Macrium Reflect, that way you have the option of reverting to Home premium if you wish to. Then follow the Anytime Upgrade guide.