Pixie, I am an early childhood teacher. Your daughter sounds completely normal to me! Actually she sounds like she's doing well if she settles after a short time. She is right in the middle of the time that children experience separation anxiety so it is noraml that she's upset. Plus being her first week, she is doing well! I know it most likely feel terrible having her crying as you leave, but it is normal.
I agree with the previous posters in that it would probably be best for you to give her a hug and kiss tell her you love her and will be back later. Tehn hand her over to her primary carers and leave. Also have a predictable routine for her from when she wakes. So wake up, have breaky, dress, brush teeth, pack bag....yada yada! But do mostly the same thing each time you go to day care. Be supportive of your child's feelings. Don't get upset or angry that she's upset. Let her know that you understand how scary it is to be separated from mum/dad without dwelling on the negative.
Above all else don't, DON'T sneak out of the room. She will wonder where you are and not know what happened or if you're coming back.
HTH. If you have any more questions, feel free to ask!! And good luck. Rmember it is only her first few weeks. It will take time for her to settle. And if they have a break over the chrissy holidays, expect that she will have the same anxiety when you go back there.