Penelope Leach, a famous British child psychologist, once said, "Independence comes out of dependency needs being met." That means that your daughter can only move away from you when she feels safe. And to do that, you have to hold her. And hold her. And hold her. Until she has been held enough -- and trust me, that will happen.
You can walk away and leave her to cry it out. However, sooner of later, you will have to deal with this clingy I-need-want-my-mommy stage. I know this first hand from raising three boys.
My first two sons are biologically mine. And I gritted my teeth and held them for during much of their first year. I always felt like I should be doing something else. I wanted them to move away from me. Now (age 15 and 12), they have no problem flying across the country to visit friends or extended family. They can move away from me.
My third son is mine through adoption. We adopted him at 3 1/2, from an orphanage in Romania. When he was an infant, no one held him. When he cried, no one picked him up. He wasn't cuddled and loved -- there were 16+ kids in his nursery. How could the one person meet all their needs?
Now he is 10 years old. He is developmentally about 2 or 3, and probably will never be able to live independently. For first three years he was home, I snuggled him every morning, held him on my lap to watch TV, spoon fed him, and sung him to sleep every night. I had to do all those things for my other sons -- but only until they could do it themselves (1 year or less). My third son took three times that long since nobody did it when he needed it.
Even today he panics if alone too long. He will come bursting from his room to find me. Then he will either drag all his toys and play at my feet or drag me into his room so he can play with them there. He doesn't necessarily want me to play with him -- he just wants me there.
Obviously, your daughter isn't going to experience the deprivation that my son experienced. You'll probably leave her once or twice to cry it out when you can't stand it anymore (I did that with all three boys!) But, trust me, it is important. You can't imagine how important that cuddling, rocking, holding, loving is.
And I haven't even talked about the benefits to your daughter's gross and fine motor development . . . balance skills . . . language skills. . .
Just hold her.