Currently Being ModeratedMay 3, 2013 8:43 AM (in response to Maeve83)
Welcome to the Support Communities. You can easily back up your current phone to a new computer, then restore that back up to your new phone. There are a few steps to go over first. Make sure that no phones are plugged in.
Open iTunes Preferences and select the Devices tab. Select the option to prevent iPods, iPhones, and iPads from syncing automatically. Make sure the box is checked so that the phone will not sync when plugged in.
Then follow the steps on this article on the back up process.
iOS: How to back up
in this article it will go over on how to restore from those backups.