It all depends...
FYI, I also moved couple of weeks back.. 2 days after I moved, INS sent FP notice to me that was re-directed by the Post Office. Whereas my wife's H4 extension was approved just 3 days after our move, obviously it went to my old address and not re-directed so far by the Post Office.
So in any case just call up and change your address in addition to sending the AR-11 form.
These are the things you need to do with INS when you move.. ( in addition to lots and lots of stuff you do when you move)
1. Send completed AR-11 from (i guess the postal address is London, KY) for each one in your family in separate envalops by certified post. This way you have proof that you have sent. Also take copies of all AR-11s.
2. Send Copy of AR-11, Copy of your receipts for the cases that are pending with INS, and a cover letter, to your service center.
3. Call INS 800 number and update the address
Here are the details to follow when updating address (assuming you do not speak espanol)
Call (800) 375-5283
press 1
then
press 1
then
press 2
then
press 9 to talk to a customer service rep.