Yes, animals have spirits (see D&C 77:2–3). Of course, there is a major difference between animals’ spirits and our spirits—we are begotten sons and daughters of Heavenly Father, and they are not.
And according to the Prophet Joseph Smith, there are at least some animals in heaven. He said:
“John saw curious looking beasts in heaven; … actually there, giving glory to God. … (See Rev. 5:13.) …
“I suppose John saw beings there 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. 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” (in History of the Church, 5:343).
So, although we don’t have a complete understanding of what happens to animals after they die, we believe that they will enjoy some kind of salvation and immortality.
Author: Packard, Sandra Bradford
Latter-day Saints believe that animals, like humans, have spirits, in the form of their bodies (D&C 77:2). Like humans and plants, animals were created first as spirits in heaven and then physically on the earth (Moses 3:5). Mortal and subject to death, animals will be saved through the Atonement of Christ (TPJS, pp. 291-92). Humans and animals will eventually live in peace on this earth (Isa. 11:6-9; 2 Ne. 30:12-15; D&C 101:24-26). The Prophet Joseph Smith taught that animals will be found in heaven, in myriad forms, from myriad worlds, enjoying eternal felicity, and praising God in languages God understands (TPJS, pp. 291-92).