Breastfeeding definitely works for soothing -- it has everything a baby needs! Think of it - for the past 9 months, your baby has been completely surrounded by you, cuddled by you constantly, nourished by you, hearing your voice and your heartbeat, etc. Breastfeeding allows you to continue this experience as much as possible outside the body. Don't worry about "spoiling" her -- she's too young for one thing, and it's not "spoiling" to attend to her needs and let her know that you're there for her. It's comforting to her to know that you're there. It's a big world she's been born into, and all she knows about it is you, so when you're not there, her whole world is gone. Enjoy that and embrace it - before you know it, she'll be exploring that big wide world.
It's easy to overstimulate newborns. But carrying baby around in a sling or other carrier, and nursing her is not overstimulation. Constantly waving rattles in her face may be. :-) When baby breaks off eye contact or is looking away from what you're trying to interest her in, she's probably overstimulated. Don't fret, but just be there.
Some scientists who study both humans and animals will say, that based on various characteristics of different mammals, humans born at 9 months are "premature" compared to, say, full-term monkeys, kittens, horses, etc. They suggest that babies need "kangaroo care" for "the fourth trimester" - the first three months of life, when their bodies are still so immature in so many ways. Getting a carrier will allow her to get what she needs (you!), while still allowing you to do what you need to do. You've got years to work at instilling good habits in her; allow her these few months to just grow and be loved.