I highly recommend the Roundhouse Baby Carrier. (http://roundhousedc.com/) It's as easy to use as a sling but the buckle is much more secure than on those ring slings so you don't have to keep adjusting. I used mine from birth until close to 18 months--it's rated up to 3 years or 35 pounds. You can wear your baby 6 different ways. You can see how-to videos on the website. It goes through the wash like a champ and I even went through the airport by myself when my son was around 5 or 6 months with a big suitcase and car set and stroller in tow! (car seat on stroller, stroller in front of me, suitcase behind, son in carrier and off we go!) I couldn't have survived with my carrier!
Since your baby is so small, I wonder if laying a folded receiving blanket under her in the carrier, sort of like a platform, would help give her a little more mass in the carrier. (my pondering only, I haven't seen that recommended anywhere.)