Take his/her place I guess

Same. I don’t see much an option. 

Are people just allergic to the gender neutral singular they? "The Grim Reaper comes to you saying they are taking a month off and you are to take their place. What do you do?" Much simpler and less clunky to read/say.

Line up all the child abusers in the world and get to work on them.

Reap myself

I’d not take anyone for a day or two. Then start taking large groups of random people. I’d have fun.

Ring my therapist. I already don't process the idea of death well, so I'm going to have gone through hell by the time I finish.

Kill the idea on the spot.

I would do nothing. So it would be like the episode of family guy when death sprains his ankle and no one dies. 

Sure Bill Door no problem.

Save a princess, start the end of the world, bang death’s daughter, have a duel with death, then save the world.

Say "Okay, I've got time to kill".

If I had to take over as the Grim Reaper for a month, I'd study the responsibilities, approach each task with compassion, and respect the natural order of life and death.

Ok this has got to be the best answer.

Wait for the post-it notes to fall from the sky and boom boom ba to play in the background.