Make a backup of your old iPAd to itunes or iCloud.
Then restore from that backup when setting up the new iPad Air.
The restore will put your data onto the new iPad. (The Os will remain at 7).
Folder structure is a little iffy. Since backups don't restore Apps, only data, you would still need to re-download the Apps to the new Air and as such would need to create the folders for them.
Apple wrote:
- Camera Roll (Photos, screenshots, images saved, and videos taken.
Note: For devices without a camera, Camera Roll is called Saved Photos.
- Contacts* and Contact Favorites (regularly sync contacts to a computer or cloud service such as iCloud to back them up).
- Calendar accounts and subscribed calendars.
- Calendar events.
- Safari bookmarks, cookies, history, offline data, and currently open pages.
- Autofill for webpages.
- Offline web application cache/database.
- Notes.
- Mail accounts (mail messages are not backed up).
- Microsoft Exchange account configurations.
- Call history.
- Messages (iMessage and carrier SMS or MMS pictures and videos).
- Voicemail token. (This is not the voicemail password, but is used for validation when connecting. This is only restored to a phone with the same phone number on the SIM card).
- Voice memos.
- Network settings (saved Wi-Fi hotspots, VPN settings, network preferences).
- Keychain (this includes email account passwords, Wi-Fi passwords, and passwords you enter into websites and some other applications. If you encrypt the backup, you can transfer the keychain information to the new device. With an unencrypted backup, you can restore the keychain only to the same iOS device. If you are restoring to a new device with an unencrypted backup, you will need to enter these passwords again.)
- App Store Application data (except the Application itself, its tmp and Caches folder).
- Application settings, preferences, and data, including documents.
- In-app purchases.
- Game Center account.
- Wallpapers.
- Location service preferences for apps and websites you have allowed to use your location.
- Home screen arrangement.
- Installed Profiles. When restoring a backup to a different device, installed configuration profiles are not restored (such as accounts, restrictions, or anything which can be specified through an installed profile.) Any accounts or settings that are not associated with an installed profile will still be restored.
- Map bookmarks, recent searches, and the current location displayed in Maps.
- Nike + iPod saved workouts and settings.
- Paired Bluetooth devices (which can only be used if restored to the same phone that did the backup).
- Saved suggestion corrections
- Trusted hosts that have certificates that cannot be verified.
- Web clips.
