This has been discussed on a couple of topics recently, so I thought I would make a special topic for it. Let's start with what St Thomas says on the Resurrection of the dead (I have excerpted):
Supplement (Question 75 and 81):
The heavens will never be broken as to their substance, but as to the effect of their power whereby their movement is the cause of generation and corruption of lower things: for this reason the Apostle says (1 Corinthians 7:31): "The fashion of this world passeth away." (Q81, Article 1 - reply to objection 1)
Further, the resurrection is necessary in order that those who rise again may receive punishment or reward according to their merits. Now either punishment or reward is due to all, either for their own merits, as to adults, or for others' merits, as to children. Therefore all [good and evil] will rise again. (Q75 Article 2)
Further, man will rise again at the most perfect stage of nature. Now human nature is at the most perfect stage in the age of youth. Therefore all will rise again of that age [which Thomas takes to mean around 32 or 33]. (Q81, Article 1)
Further, at the resurrection God will restore man to what He made him at the creation. Now He made woman from the man's rib (Genesis 2:22). Therefore He will also restore the female sex at the resurrection. (Q81 Article 3)
Consequently those natural operations which are directed to cause or preserve the primary perfection of human nature will not be in the resurrection: such are the actions of the animal life in man, the action of the elements on one another, and the movement of the heavens; wherefore all these will cease at the resurrection. And since to eat, drink, sleep, beget, pertain to the animal life, being directed to the primary perfection of nature, it follows that they will not be in the resurrection. (Q81, Article 4)
So - in summary:
1. The heavens will remain as they are but the motion of the stars and planets will cease.
2. The earth will be populated not just by the good - but also the evil.
3. We will all be around the age of 32 or 33.
4. Both male and female forms will exist.
5. Movement will cease, we will not eat, drink, sleep, have children, etc.
So, it would seem to me that (particularly as regards item 5) there will be nothing on the earth which exists solely for the "animal" aspects of our survival - namely plants and animals. For the record, my scholastics professor told us in class the same thing. Because some here are not convinced I thought it would be useful to quote the above Aquinas quotes to show how it is reasonable to believe that animals and plants will be excluded from the earth of the resurrection of the body - their function is to clothe and feed us - neither of which things are necessary in the resurrection.