Why are you putting her down quickly?

Babies have a reflex (called the Moro reflex) that makes them startle and spread theirs arms when they feel like they are falling. They feel a lone and unprotected, insecure. She is expected to throw her arms and legs out and extend her head in fear: it's normal.

I am not sure about the eye fluttering. It could be part of the reflex or it could be something else. I don't think it is reason for alarm since the baby is happy, but you should bring up your concerns at the baby's next check up (which should be at 2 months.)