Sleepy baby won't sleep

My 9 month old has been awake for 4 and a half hours, she's been yawning & rubbing her eyes & getting fussy.. and yet everytime I go to rock her to sleep her head jolts up and she refuses to sleep I've tried putting her down & she just cries.. should I just let her cry it out? Or should I keep her up (I'm worried if I do she'll go past the point of no return & she won't sleep tonight.. also she's had plenty to eat so she's not hungry..