Breast feeding and pacifiers

My daughter is a week old and will only fall asleep if she's latched on. She'll eat and I know she's full but will wake up only to want to eat again but will fall asleep within a minute after latching. She tries to suck on her fingers and at this point i want to try and give her a paci. She's my first baby so I'm totally lost as to what to do. Is this normal behavior for a new born ?