JANN - What happens to beloved pets in the afterlife?

JOEL - The scriptures tell us that God created the spirits of all living things before they were created naturally on the earth:

"And now, behold, I say unto you, that these are the generations of the heaven and of the earth, when they were created, in the day that I, the Lord God, made the heaven and the earth.
And every plant of the field before it was in the earth, and every herb of the field before it grew. For I, the Lord God, created all things, of which I have spoken, spiritually, before they were naturally upon the face of the earth." (Moses 3:4-5)

Anything that has a spirit and a physical body will eventually die causing separation of the physical from the spiritual.
The scriptures also say:

"For since by man came death, by man came also the resurrection of the dead.
For as in Adam all die, even so in Christ shall all be made alive." (1 Cor 15:21-22)

Anything that dies involving separation of body and spirit will again be made alive or resurrected, including all animals.

"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.)

President Joseph Fielding Smith said:
"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, vol. 2)

The Prophet Joseph Smith was asked this question: "What are we to understand by the four beasts, spoken of in the same verse?" (i.e., Revelation 4:6.) His answer is as follows:

"They are figurative expressions, used by the Revelator John, in describing heaven, the paradise of God, the happiness of man, and of beasts, and of creeping things, and of the fowls of the air; that which is spiritual being in the likeness of that which is temporal; and that which is temporal in the likeness of that which is spiritual; the spirit of man in the likeness of his person, as also the spirit of the beast, and every other creature which God has created." (D&C 77: 2-3)

Again when commenting on the Revelation of John, the Prophet said:
"John saw curious looking beasts in heaven, he saw every creature that was in heaven . . . actually there, giving glory to God. How do you prove it? (See Rev. 5:13. ) "And every creature which is in heaven, and on the earth, and under the earth, and such as are in the sea, and all that are in them, heard I saying, Blessing, and honor, and glory, and power, be unto Him that sitteth upon the throne, and unto the Lamb for ever and ever."

Joseph Smith also said:
"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. 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 will 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." (Teachings of the Prophet Joseph Smith, pp. 291-292.)

Animals are living souls, but we need to remember their place in God's kingdom:
"The Lord has said that not only has man a spirit, and is thereby a living soul, but likewise the beasts of the field, the fowl of the air, and the fish of the sea have spirits, and hence are living souls. But this does not make them kinsmen to the sons and daughters of God. They are our Father's creations, not his offspring, and that is the great difference between man and beast." (Doctrines of Salvation, vol. 1, Bruce R. McConkie, Joseph Fielding Smith)

According to all these comments and scriptures we know that animals have souls and will be resurrected and be found in heaven, but we don't really know which level of heaven they will be in after the resurrection. One might reason that since animals primarily live on instinct and can't conscienciouly commit sin; they therefore fulfill the measure of their creation, like the earth does (D&C 88:25), and sould inherit the Celsetial kingdom. Or perhaps we may see them represented in all the kingdoms.

President Joseph Fielding Smith made a rather speculative comment about this:
"As to where the beasts, birds, and fish, and all other creatures will go after the resurrection we can only express an opinion. John saw many of them in heaven in the presence of God. It is very probable that they, like mankind, will be distributed in the various kingdoms, celestial, terrestrial, and telestial. We may well believe that in each of these kingdoms such creatures will be assigned." (Answers to Gospel Questions, vol. 2)

Obviously "all dogs go to heaven", and I assume they will be in the Celestial kingdom; the rest I don't know about.