Hey guys, thanks for all the replies. You've all given some really good info. I'll provide an update to my situation.
On Friday (January 13th) I called Lego's customer service and explained that I was missing an entire bag, and had the part number of the baby's body handy just so that I could tell them what bag. The guy on the phone acted surprised but didn't seem to doubt me or ask too many questions, he said he'd send a replacement of the whole bag.
Within minutes I received the usual confirmation e-mail you get when you fill out the missing parts web form. I plugged the order number they gave me into the shipment tracker portion of the site and saw that they had each and every part from the missing bag listed on there, so I thought everything was great.
However, today (6 days later), when I plug in the order number, every one of those parts still shows "In Warehouse." Is it normal for missing parts to take this long to even leave the warehouse?
I mean I'm not expecting them to 'overnight' these parts to me or anything but I figured they would have at least left the warehouse after 6 days.