If the entire creation–not just human beings–is to be taken up into the divine life (deified, to use the term Edwards prefers), then it makes sense to ask whether individual, sentient, non-human creatures (i.e., animals) will participate in the new creation. Edwards thinks that, based on the character of the God revealed in Jesus, we can hope that animals will share in the resurrection life.
He points out that the Bible affirms God’s love for each thing that he has made. Further, the God revealed in Jesus is one of boundless compassion. At the very least, Edwards says, we must affirm that God remembers, holds in the divine mind, the travails and triumphs, sufferings and joys of each one of his creatures. But, he goes on to argue, the biblical concept of God’s memory is much more robust and metaphysically significant than our ordinary human concept. For God to remember us is for God to hold us in the divine mind, to keep the divine attention on us. Metaphysically, God’s holding us in the divine mind is what keeps us and the entire world from lapsing into non-existence. Moreover, the incarnation is God’s assumption of flesh, not just humanity. In some way, it reconciles “all things” to God, not just wayward human beings. So is there something more we can hope for in terms of animal participation in the life of the world to come?
I have been proposing that each animal is known and loved by God, is the dwelling place of the Creator Spirit, participates in redemption in Christ, and abides forever in the living memory of God. Can more be said? I think it can. It can be said that animals will reach their redemptive fulfillment in Christ. They will not only be remembered and treasured, but be remembered in such a way as to be called into new life. (How God Acts, p. 165)
Edwards admits that we can’t really form an imaginative picture of what this would be like, but, then, the same is true of the resurrection of human beings. Our inability to adequately imagine something doesn’t show that it isn’t real. As he says, the “basis for our hope is not our imagination but the God revealed in Jesus. … As Elizabeth Johnson has said, our hope is not based upon information about the future but on ‘the character of God’ revealed in the Christ-event” (p. 165). Animal fulfillment, Edwards says, must be based on their proper nature, and we don’t need to think of it as strictly parallel to human fulfillment. “The God of resurrection life is a God who brings individual creatures in their own distinctiveness in some way into the eternal dynamic life of the divine communion” (p. 165).
In some ways, the problem of animal suffering is more acute for theology than that of human suffering. This isn’t because animal suffering matters more (whatever that might mean), but because, as C. S. Lewis memorably put it, animals can neither deserve nor be improved by pain (as humans arguably can). Plus, there’s no free-will defense available for animal suffering, at least not directly. If God has the character that Christians believe he does, and if the distinctively Christian answer to the problem of evil is that God has acted and is acting to redeem his creation, then it’s hard not to draw the conclusion that God will include his beloved animals in the resurrection life.
A Thinking Reed 
George Macdonald said this:
“I know of no reason why I should not look for the animals to rise again, in the same sense in which I hope myself to rise again–which is, to reappear, clothed with another and better form of life than before. If the Father will raise His children, why should He not also raise those whom He has taught His little ones to love?
“Love is the one bond of the universe, the heart of God, the life of His children: if animals can be loved, they are lovable; if they can love, they are yet more plainly lovable: love is eternal; how then should its object perish? Must the love live on forever without its object? or, worse still, must the love die with its object, and be eternal no more than it?
“Is not our love to the animals a precious variety of love? And if God gave the creatures to us, that a new phase of love might be born in us toward another kind of life from the same fountain, why should the new life be more perishing than the new love?
“Can you imagine that, if, hereafter, one of God’s little ones were to ask Him to give again one of the earth’s old loves–kitten, or pony, or squirrel, or dog, which He had taken from him, the Father would say no? If the thing was so good that God made it for and gave it to the child at first who never asked for it, why should He not give it again to the child who prays for it because the Father had made him love it? What a child may ask for, the Father will keep ready.”
Martin Luther argued for the resurrection of animals. Here is Preserved Smith quoting the Tabletalk:
Before we leave the Black Cloister one humble inmate must not be forgotten, the little dog named Tölpel, or Clownie:—
One of Luther’s children had a dog. The doctor said: “We see now the meaning of the text, ‘Ye shall rule over the beasts of the field,’ for the dog bears everything from the child.”
Asked about the restoration of all things and whether there would be dogs and other animals in that kingdom, he said: “Certainly there will be, for Peter calls that day the time of the restitution of all things. Then, as is clearly said elsewhere, he will create a new heaven and a new earth. He will also create new Clownies with skin of gold and hair of pearls. There and then God will be all in all. No animal will eat any other. Snakes and toads and other beasts which are poisonous on account of original sin will then be not only innocuous but even pleasing and nice to play with. Why is it that we cannot believe that all things will happen as the Bible says, even in this article of the resurrection? Original sin is at fault.”
[from Preserved Smith, The Life and Letters of Martin Luther, (London: John Murray, 1911) p. 362. ]