They don't specify the exact nature of the freebies other than the baby bag and I don't see a closing date for the Enfamil Free Diaper Bag offer but there is a live help phone number at the bottom of the promotion page where you might be able to get the details.
The rules say that this offer is for residents of the United States only and that residents of Canada should enter in the Canadian Enfamil promotion. I checked the site for Canada and they do not mention getting a free diaper bag but do say that if you enter (or enroll) you will get up to $75 in free gifts that you might assume would include Enfamil formula coupons or free baby products.
Here is the address of the entry form with the rules
