Just tranferred my AT&T Unlimited Data Plan from my iPad 1 to my New iPad (3rd Gen). I went through the 1-800-331-0500 number and asked for the section which manages iPad Unlimited Data Plan transfers from old to new iPads. I was transferred (no waiting) and talked to a knowledgeable rep who walked me through the process.
Process with AT&T Rep is as follows:
1. Rep verified my old iPad information using my old iPad Cellular Number, email address, and name.
2. Directed I power down (turn completely off) my old iPad.
3. Turn on new iPad and turn off WiFi.
4. On new iPad goto Settings - Cellular Data - View Account and Log-in.
5. After log-in is a new screen with Data Plans -- ensure "Unlimited Plan" for $29.95 is checked (it should be already) -- Then press "Next" on that screen.
6. Terms and Conditions Screen -- "Agree".
7. Screen comes up indicating AT&T is updating plan.
8. Wait till that screen goes away.
9. Power Down (turn off) New iPad completely -- wait ten seconds -- restart to Apple icon on screen and let iPad reboot.
10. Upper Left screen indicates AT&T Network acquired (signal bars present) -- 4G or LTE if within range of 4G.
11. Check that you can connect with websites through Safari Browser -- Yes.
12. Back to Settings -- General -- About Screen.
13. Confirm with rep that IMEI and ICCID on iPad matches what just updated in their system.
That's it! Five Minutes and transfer complete. According to other posters this process can all be done without a customer rep. However, the rep can see what's happening in their system and confirm everything transferred correctly and that service continuity is maintained. In the unlikely event a problem occurs they can help sort it out immediately.