When can I discard the Death Creeper Card?
I disagree with the other answer.

The card text says:


  If you have this at the start of your turn, discard something else you have in play (a Keeper or a Creeper). You may discard this anytime it stands alone.


This card has two effects:


The first effect, discarding something in play, must take place at the start of your turn (as accurately explained in the other answer).
The second effect, being able to discard Death itself, can be done at "any time".


I believe the second is the effect you are asking about. That means that if, at any point during anyone's turn, that is the only card you have in play, you may discard it. To answer your specific scenario. If you draw it (and automatically play it) and it is the only card in front of you, you can discard it immediately.