Death and creationism
Without getting into New Testament minutiae, I'd like to point out a problem. I'm sure people have thought about this, but I'd like some feedback.
I assume it comes from Genesis 2, which says:
 And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat:But if we skip down, we find that Adam and Eve eat the fruit of the Tree of Knowledge of Good and Evil:
 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
 And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:So, how do you read that and not see eternal life coming from the (uneaten) Tree of Life?
 Therefore the LORD God sent him forth from the garden of Eden, to till the ground from whence he was taken.
The obvious reading of the first quote is that God is blustering a little, making a threat that He'll strike Adam down right then and there if he breaks this one, simple rule. Adam slips up, but God is a bit of a softie, and decides to let it slide.
Besides, even if Adam and Eve were immortal, why should the animals be, too?