Isaiah 11:6-9 seems to imply to some that the "curse" has been removed, and that there is a return to Paradise. When comparing these scriptures to other scriptures in The Bible, it might be interesting to quote those, as well. Isaiah 11:6-9 seems to be referring to the Millennium, and not Eternity.
Isaiah 65:25 says:
The wolf and the lamb shall feed together, and the lion shall eat
straw like the bullock: and dust shall be the serpent's meat. They
shall not hurt nor destroy in all my holy mountain, saith the LORD.
My view is that the New Heavens and Earth will come during the Millennium, because of the order of which Jesus Christ said that this would happen wouldn't make sense (from what I understand) if there was a "new heavens and new earth" after the Millennium, for a multitude of reasons. Here's one of those reasons:
Isaiah 65:17 says:
For, behold, I create new heavens and new earth: and the former shall
not be remembered, nor come into mind.
If you read down to verse 20, it says:
There shall be no more thence an infant of days, nor an old man that
hath not filled his days: for the child shall die an hundred years
old; but the sinner being an hundred years old shall be accursed.
If the 'new heavens and a new earth' comes after the Millennial Reign of Jesus Christ, then how does one reconcile death here in this passage? This is referring to Millennial conditions and not Eternity. (ref. Revelation 20:1-3). Yes, the extension of the length of a person's life is great, but there's death, and so this could not be referring to Eternity.
Isaiah 66:22 says:
For as the new heavens and the new earth, which I will make, shall
remain before me, saith the LORD, so shall your seed and your name
There is also biblical references on the 'vegetation', as well, during this time (Hosea 2:20-22; Isaiah 30:23-26, and Ezekiel 24:25).
As for animals being in the new heavens and the new earth, from the passages in Isaiah above, the answer is a resounding 'Yes!' (as others have pointed out).