Congratulations on your new baby!  I know she is the joy of your life.  I can't really give you personal experience – although I had three children, they were born well before my pain problems began.  However, I do know what strain little ones can put on even a healthy back. 

You might consider seeing a physical and/or occupational therapist.  They should be able to teach you the best ways to lift and carry your baby to reduce the strain on your back.  A physical therapist should also be able to give you some exercises to help strengthen your back.  Your baby is only going to get bigger and she's still going to want mommy to pick her up and hold her when she's two and three years old.  So the sooner you learn the best way to do it, the better for you.  In the meantime, I found a few tips from the American Academy of Orthopaedic Surgeons that may be helpful – mostly for lifting her.  Here's the link:  http://orthoinfo.aaos.org/topic.cfm?topic=A00264

I also found what is supposed to be the top 10 baby carriers for back pain.  Be sure to read the reviews as a few seem to have some negative reviews even though they're high on the list.  Hopefully this can help you decide which would be best for you.  Here's the link:  http://wize.com/baby-carriers/t6486-back-pain

I wish you many happy, healthy years as you raise your little girl.