It's more that no scripture places animals in heaven.
But we do have scripture which helps us to know this:
Eccl 3:19-21
19 For that which befalleth the sons of men befalleth beasts; even one thing befalleth them: as the one dieth, so dieth the other; yea, they have all one breath; so that a man hath no preeminence above a beast: for all is vanity.
20 All go unto one place; all are of the dust, and all turn to dust again.
21 Who knoweth the spirit of man that goeth upward, and the spirit of the beast that goeth downward to the earth?
KJV
Man's spirit goes up to heaven, but the spirit of animals go downward. It's God's way. I trust that God knows what's best.
The only mention of an animal in the eternity chapters of Revelation is the Lamb, which is Jesus Christ and not a literal lamb.