What kind of error are you getting? I'm guessing you're getting an error because the object doesn't exist??
If so, change your instance_destroy() line to:
if instance_exists(obj_enemy) then instance_destroy(obj_enemy);
Hope that helps, let me know if that doesn't help.. and if it doesn't please let me know what kind of error you are getting.
Also, just a heads up.. your code is going to cause you problems as your game gets more advanced..
You probably don't want to kill the enemy object just because the player died. That seems silly to be honest, but I don't know what kind of game you are making either. In most situations, that would be really silly.
My suggestion to you is to instead have code in the enemy object to keep track of it's own health and destroy itself when it's health goes below zero.
So for example let's say that as your game develops more, your player starts out with a regular bullet type and it will kill that enemy object, but maybe in time you add a ice bullet (just an example) but you decide that because this ice bullet fire much faster and all that you want that enemy object to take 2 or 3 shots to be killed by the ice bullet. So in the collision with the regular player bullet in the enemy object collision check with it, you might have 50 damage be done. Let's also pretend that you've set the enemy object in its create event to have a "my_health = irandom_range(35, 45)" line that sets it to have a random health amount between 35 and 45. So we know that the players first bullet, just one hit should destroy it. You have a line of code that simply checks to see if its "my_health" has dropped to zero or below as in "if my_health <= 0 then instance_destroy();" Again that check needs to be in its step event.
Now, for the ice bullet you added in my example, your enemy object would have a collision check with that and code that perhaps says "my_health -= 15" or whatever you want to set the damage at. Now when your enemy object takes hits from 3 ice bullets, it should be dead. Want it to take randomly between two or three hits from ice bullets to die? Easy, just increase that damage in the collision with the ice bullet to 20 damage!
..I hope that makes sense.