First - congratulations on becoming a mom! It will truly be the toughest job you will ever love.
It is not uncommon for some children to go through separation anxiety at various stages in the infant and toddler periods. You just have to remember that you're the Mom and you set the rules. One thing is for certain, any "habit" or behavior you permit becomes harder to break the longer you wait.
Having said that, though, your daughter is still an infant who needs lots of love, and she knows where her security lies - with you. As a loving and concerned mother (which by asking for help you show you are) you can use your instincts to know when enough is enough - when the cry for attention is a real need or an excessive demand.
You are at the very early stages of "discipline" where your daughter needs to learn that just because Mommy is there, she does not get 100% of Mommy's time and attention. This will be especially important as she gets to be a toddler that will have to share Mommy with another sibling. This is hard to do when you're a first time mom, you have the time, and there's only one child.
If you have tended to your daughter (given her what she needs plus some TLC) and there is no special condition like colic or being sick or scared, then you just have to let her cry. You can reassure her with a calm voice that she is okay, you're right there, and she's all right. Make sure she has something to do like play in the exersaucer or with some toys or a mobil, and then let her be. Do not feel like you are hurting her, neglecting her, or reaking havoc with her emotional state by "ignoring" her demanding cries. She is learning that she is not the only thing in your universe and that just because Mommy isn't holding her she will still be okay.
I often tell my friends that child #1 is more about training the parent than the child. It's process that every parent must go through - even if you spent your life being around or taking care of other babies. It will take some trial and error but you need to find a balance between time you give to your children and time you give to yourself. If you don't, you won't have the energy to deal with these "battles".
I hope this helps.
S. L.