jcli0002, it is correct that it won't hurt to apply for EAD even if you have a H-1B. EAD is free if you applied for I-485 after July 30, 2007 and it has no influence on your H-1B status. Well, you'll have to pay for two more passport pictures, make another copy of your I-94, and fill in the very simple form I-765. And pay for another envelope and postage if you apply after you've sent the I-485 application (and include a copy of your I-485 receipt notice I believe?). So it'll cost you a couple of bucks and will take an hour or two to complete carefully. But looking at the colorful sparkling hologram on the card is so well worth it.
That said, as TheRealCanadian alluded to, you might as well also apply for AP (otherwise you can't travel outside the country if you're no longer in H-1B status, before your GC arrrives). Also for free.