Isaiah chapters 7-12 are part of a series of prophecies about the deliverance of Israel from Syria, and Assyria and that such deliverance would come through Messiah (Isa 9:1-7) and that Israel will need continuing corrective punishment (9:8-10:4) and Assyria would fall due to the rod of God's anger (10:5-34).
Isa 11 describes the Messianic kingdom in three sections:
- Deliverance and restoration through Messiah (11:1-9)
- The gathering of the gentiles and the Jewish exiles (11:10-16)
- A song of deliverance (Isa 12)
Note that much of Isa 11 about the coming Messiah is:
- Quite symbolic/metaphorical language ("branch", "root", "his breath will slay the wicked", "belt of righteousness", etc.)
- The Messiah discussed concerns Jesus' 1st advent as it discusses the returned exiles from the (still future in Isaiah's time) Babylonian captivity (11:12ff)
- The prophecy is clearly the ideal outcome that might have been if the Jews had accepted Messiah and been faithful. This was not the case.
It is an interpretation in some circles to read Isa 11:6-9 as literal and make it about either the New Earth or heaven. Such an interpretation would have the effect of taking an isolated passage and reading it literally despite its figurative surroundings, and, placing it in a time that it is not intended to discuss (after Jesus' second advent). Quite a stretch!
This is not to suggest that such an interpretation is wrong - only that a secondary application is valid here on the basis of no data in the text itself to allow such.
This is confirmed by the phrase "My Holy Mountain", an Old Testament phrase that means Mt Zion on which literal Jerusalem is built. Ps 2:6, 3:4, Jer 17:3, Eze 20:40, Joel 2:1, 3:17, Obad 1:16, Isa 65:25, 66:20, Dan 9:20, etc. Again some of these, as some have suggested, speak of heaven or the New Earth - again by asserting a secondary application. The justification advanced for this is to say that most of these idealised prophecies were never fulfilled (this is correct) and therefore they will be fulfilled in heaven or the New Earth But this remains an assumption.
Lastly, will animals be in heaven? On the basis that the earth will be remade to restore the original creation (eg, Rev 21, 22, etc), and that animals were in Eden, I believe that animals will be in heaven or the New Earth.
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 remain.
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).