I am in your situation. Read on another site the following:
Go to att.com/ipadlanding, login to your account and adjust your account to reflect the iPad LTEs IMEI and SIM card number.
I did this from iPad 1 to 2 and it worked flawlessly.
I will be doing it 3/16 so fingers crossed.
One of the main things mentioned in another section is to completely power down all the iPads in question so the transfer can occur cleanly.
I already checked this site out, and there is a spot to update your device info.
Here is what I am planning on doing next Friday:
1- Power down completely iPad 1.
2- From the unopened box of new iPad grab the information (IMEI and SIM card number) and update that in the unlimited data account information at the ATT site.
3- Power on new iPad. Confirm settings are correct for unlimited data, etc.
4- Power on iPad 1.
5- Set up new email address/password following the procedure on the actual iPad for adding a data plan (I remember this being fairly easy the first time).
I am pretty sure that I cannot get unlimited with both iPads, but would be nice!
Someone mentioned that the SIM card may be completely different so switching it out may not work correctly.