If you have not read Stories Versus Truth, you may want to read that before reading this.

Since all plant life had been destroyed and there was also no animal life, what did the herbivores eat?  What did the carnivores eat? If they ate the smaller species, then that would have led to the extinction of a lot of species since there were only 2 of each on the ark.

These questions pose no real challenge to the Bible.  The animals were created as herbivores, not carnivores.  Fossil evidence from the flood gives us evidence that some animals had started to eat one another, though we cannot know how widespread this disorder had become.  It is very possible and likely that all the animals on the ark were herbivores.  For adequate food to have sprung up by the time the animals left the ark is a very reasonable assumption.

Let us dispose of Naturalism and all its presuppositions.  Jesus Christ holds everything together at all times.  The tremendous regularity and predictability of the way that He does this is what makes science possible.  The entire flood was a miraculous event.  God brought the animals to the ark.  God closed the door of the Ark.  We know this by revelation.  We don't know what else God did.  If God had chosen to provide for the animals after the flood by supernatural means, what of it?

The skeptic wishes to attack the Bible and show it to be a flawed work.  For this reason, the skeptic is compelled to use poor thinking to show himself or herself supposed errors.  The motivation for this is that the skeptic does not want to obey God.  And God will allow the skeptic to stay in rebellion.  God will allow the skeptic to choose to go through judgment rather than to submit to God.

In order to be logical and rational (sane), the skeptic must realize that showing the Bible to have an error would involve finding some part of the Bible that says something for which no explanation could possibly be given.  This has never been done, but skeptics are satisfied if they can find just one person who does not know the answer.  The fact is that there are some things that God calls mysteries.  These are things that He has not yet revealed.

See also:

http://creation.com/the-carnivorous-nature-and-suffering-of-animals

http://www.icr.org/index.php?module=articles&action=view&ID=1205

http://creation.com/feeding-carnivores-on-the-ark-and-refuting-an-accusation-of-closet-scientism

http://x-evolutionist.com/noahs-ark-and-the-global-flood/#3