Hello!!
If she isn't crying when you lay her down, then it is ok to leave the room. Try not to worry about doing the "wrong" thing...as there really is no real "right" or "wrong". Just go with what you FEEL is "right".
As far as activities go for a 6 week old, her activity time will probably mostly consist of feeding, diaper changes and some cuddling.
Congrats on your little one!!