Many LDS commentators have argued that not only humans but animals will be resurrected. While this has often been lampooned, this is actually not a view unique to LDS theology.
Douglas Wilson, a Reformed Presbyterian author and apologist, addressed this briefly:
Wilson makes reference to “seed” (σπερμα) in 1 Cor 15; here is the text in question:
But God giveth it a body as it hath pleased him, and to every seed his own body. All flesh is not the same flesh: but there is one kind of flesh of men, another flesh of beasts, another of fishes, and another of birds. There are also celestial bodies, and bodies terrestrial: but the glory of the celestial is one, and the glory of the terrestrial is another. There is one glory of the sun, and another glory of the moon, and another glory of the stars: for one star differeth from another star in glory. So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption: It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power: It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body. (1 Cor 15:38-44)
Ex-Mormon activist, Richard Packham, in an article "Animal Resurrection in the Teachings of Mormon Prophets," has a good listing of quotations from LDS leaders affirming "anima resurrection":
Prophet Joseph Smith:
John saw beings there [in heaven] of a thousand forms, that had been saved from ten thousand times ten thousand earths like this,-strange beasts of which we have no conception: all might be seen in heaven. The grand secret was to show John what there was in heaven. John learned that God glorified himself by saving all that his hands had made, whether beasts, fowls, fishes or men; and he will glorify himself with them.
Says one, "I cannot believe in the salvation of beasts." Any man who would tell you that this could not be, would tell you that the revelations are not true. John heard the words of the beasts giving glory to God, and understood them. God who made the beasts could understand every language spoken by them. The four beasts were four of the most noble animals that had filled the measure of their creation, and had been saved from other worlds, because they were perfect: they were like angels in their sphere. We are not told where they came from, and I do not know; but they were seen and heard by John praising and glorifying God. [See Rev.4:6] - - General Conference held on the floor of the Nauvoo Temple, April 8, 1843 HC 5:343-44, cited in McConkie, Mormon Doctrine 1st ed p 578, and in Teachings of the Prophet Joseph Smith 345-346
Prophet Joseph Fielding Smith:
Animals do have spirits and that through the redemption made by our Savior they will come forth in the resurrection, to enjoy the blessing of immortal life. - "Answers to Gospel Questions" Volume 2, Page 48
Apostle Bruce R. McConkie:
Nothing is more absolutely universal than the resurrection. Every living thing and being will be resurrected. "As in Adam all die, even so in Christ shall all be made alive." (1 Cor. 15:22.)....
Just as the creative and redemptive powers of Christ extend to the earth and all things thereon, as also to the infinite expanse of worlds in immensity, so the power of the resurrection is universal in scope. Man, the earth, and all life thereon will come forth in the resurrection. And the resurrection applies to and is going on in other worlds and other galaxies.
Thus saith the Lord: "And the end shall come, and the heaven and the earth shall be consumed and pass away, and there shall be a new heaven and a new earth. For all old things shall pass away, and all things shall become new, even the heaven and the earth, and all the fulness thereof, both men and beasts, the fowls of the air, and the fishes of the sea; And not one hair, neither mote, shall be lost, for it is the workmanship of mine hand." (D. & C. 29:23-25.) - Mormon Doctrine 1st ed 573-578, 2nd ed 642-643
The First Presidency (Joseph F. Smith, John R. Winder, Anthon H. Lund):
He made the tadpole and the ape, the lion and the elephant but He did not make them in His own image, nor endow them with Godlike reason and intelligence. Nevertheless, the whole animal creation will be perfected and perpetuated in the Hereafter, each class in its 'distinct order or sphere,' and will enjoy 'eternal felicity.' That fact has been made plain in this dispensation (D&C 77:3). - Church First Presidency Message, Christmas greetings, Dec. 18, 1909
Apostle Joseph Fielding Smith (later President):
The Lord created all things for a purpose. Nothing has he created to be destroyed, but that all things might endure forever... The Lord intends to save, not only the earth and the heavens, not only man who dwells upon the earth, but all things which he has created. The animals, the fishes of the sea, the fowls of the air, as well as man, are to be re-created, or renewed, through the resurrection, for they too are living souls. - General Conference, October 1928
Apostle Joseph Fielding Smith (later President):
Every creature has a spirit, and that it existed in the spirit before it was on the earth; the spirit of every creature is in the form of its temporal, or mortal, body. Since this is true, and all forms of life partook of the effects of Adam's fall, therefore they are entitled to the resurrection and shall live again. "And not one hair, neither mote, shall be lost for it is the workmanship of mine hand," said the Lord. (D. & C. 29:25.) Likewise the earth, which is a living body, must die "in like manner" as to all other mortal things, and then receive the resurrection. (Isa. 51:6.) The fact that the spirit of every animal, every fish, every fowl of the air, is in the likeness of its body, and that also it was created in the spirit in the beginning, is a contradiction of these unscientific theories which man has inflicted upon a fallen world. "Church History and Modern Revelation", Published by The Council of The Twelve Apostles of The Church of Jesus Christ of Latter-Day Saints, 1946.
For the children: "Will robins go to heaven?"
"I can only tell you what the scriptures say about it," Daddy replied. "Usually, when we talk about the resurrection, we think of people. But the scriptures teach us that man, the earth, and all the life upon it will be resurrected, mentioning especially the beasts, the fowls of the air, and the fishes of the sea. The Savior gave His life so that everything would rise from the dead, even lizards and robins." - "Will Robins Go to Heaven?" - Church Friend, Apr. 1982, p. 39