I run a playgroup and see this all the time, as everyone else has said, its a way of manipulating you (yes she also doesn't want to be parted from you but this is a lesson she'll need to learn) If you were to give in and quit your job, that will only teach her that whatever behaviour / tantrums she shows at nursery is the way to get whatever she wants from you... and you would be shooting yourself in the foot for future lessons. She's not been there long. I find that a lot of the children just dont click straight away that mummy/daddy WILL always come back to get them... I would recommend some light hearted chats the night before about the structure of the day to come for example... 'Tomorow after we have breakfast we're going to get in the car and go to nursery, wont that be good! And when your there, you'll play with the toys and maybe paint me a lovely picture then after you have had your snack il come back to get you and see your picture!' If she starts to 'stress' at this convo, dont go into it anymore, change the subject and always act as if you expect her to always go to nursery.... I find that the kids at my playgroup are so well behaved because we EXPECT them to be... so by you stressing 'pre-nursery drop off time' will give her an excuse to act up, take her in, all happy and cheerful, drop her coat off, biiiiig kisses for mummy, hand her over and give lovely happy smiles and waves and then walk out... after doing this 2 - 3 times, it'll all click into place!
Dont fret, classic behaviour that always gets sorted!!