It seems like all the information on this subject is a bit ify, but this is what i have gathered so far.
In order for a monster to drop a creature card it most be the same creature and most be over level 30. (example: all Blue Pixies, Furys, Crystals etc over level 30 drop Blue Pixie cards.)
From what i have gathered the drop rate for the common pets (Yetis, Blue pixies, Red Pixies, Orcs, Skeleton, and Sirens) is about .12%. Which means about 1 in every 1000 drop a card.
Also the drop rate decrease if your character is higher than the monster you are killing.
P.S. As far as anyone can tell, your luck stat has nothing to do with drop rate.