Daniel asked in a comment below, "[W]hat does the Orthodox Church teach concerning the eternality, if any, of animals?" It is something I have thought about myself. The Scriptures and the Tradition are not overflowing with information on the subject. The great vision of the New Jerusalem in Saint John's Apocalypse is strangely silent on the fate of these companions of ours for whom we struggle and pour out our care, and who, sometimes, provide our sustenance. For a vision of animals and the Kingdom, we must go back to the Prophet Isaiah:
The wolf shall dwell with the lamb, and the leopard shall lie down with the kid, and the calf and the lion and the fatling together, and a little child shall lead them. The cow and the bear shall feed; their young shall lie down together; and the lion shall eat straw like the ox. The sucking child shall play over the hole of the asp, and the weaned child shall put his hand on the adder's den. They shall not hurt or destroy in all my holy mountain; for the earth shall be full of the knowledge of the LORD as the waters cover the sea.
Isaiah 11 6-9.
The vision of Isaiah encompasses a renewed Creation where other creatures, themselves renewed, have a place. It does not answer however, the question of the fate of individual animals. Do all dogs go to heaven? We do not know. What we do know is that all things are embraced by the love of God who keeps track of the fall of a single sparrow. In Orthodoxy, when we wish to know what God is like, and to understand what God is doing, we can look to the Saints, those men and women who lived in close communion with God. The goal of Orthodox spirituality is theosis, a participation in the life of the Trinity, whereby men and women become God-like, or as the Tradition sometimes puts it, "gods by grace." One ancient Saint that many modern Orthodox turn to as a kind of touchstone for the spiritual life is Isaac the Syrian. He had this to say about the nature of the person who has made the Divine compassion his own:
An elder once asked, 'What is a compassionate heart?'. He replied: 'It is a heart on fire for the whole of creation, for humanity, for the birds, for the animals, for demons and for all that exists. At the recollection and at the sight of them such a person's eyes overflow with tears owing to the vehemence of the compassion which grips his heart; as a result of his deep mercy his heart shrinks and cannot bear to hear or look on any injury or the slightest suffering of anything in creation. 'This is why he constantly offers up prayer full of tears, even for the irrational animals and for the enemies of truth, even those who harm him, so that they may be protected and find mercy. 'He even prays for the reptiles as a result of the great compassion which is poured out beyond measure- after the likeness of God- in his heart'.
From 'DAILY READINGS WITH ST. ISAAC OF SYRIA'- 1990 Templegate Publishers, Springfield, ILL
If the compassion of the Saints is such, how can we doubt the compassion of the God whose likeness they bear? While I know of no specific revelation concerning the animals we have loved, I do know from the Orthodox Tradition, that in God's mercy, no love is ever wasted.