When you are logging in to the new device there should be an option to perform a backup retrieval from your Google Account. This also works for if you need to perform a factory reset of the device at a later time.
On a side note about that, if you think that an application is causing your device to malfunction and a complete reset is the only cure, be sure to pay attention as the applications are reloading so you can cancel the install and avoid a repeat situation.