Scripture does not exclusively tell us whether our pets will make it to heaven. However, the Bible does provide us with some significant clues that animals will inhabit the new heaven and the new earth.
First, the Garden of Eden was populated by animals, thus there is a precedent for believing that Eden restored will also be populated by animals.
Furthermore, the Scriptures — from first to last — suggest that animals have souls. Both Moses in Genesis and John in Revelation communicate that the Creator endowed animals with souls (see Gen. 1:20,24; Rev. 8:9). Throughout the history of the church, the classic understanding of living things has included the doctrine that animals, as well as humans, have souls.
Finally, while we cannot say for certain that the pets we enjoy today will be resurrected in eternity, I am not willing to preclude the possibility. Some of the keenest thinkers — from C.S. Lewis to Peter Kreeft — are not only convinced that animals in general, but that pets in particular, will be restored in the resurrection.
Dr. Kreeft, for example, is convinced that animals will exist throughout eternity. "Are there animals in Heaven? The simplest answer is: Why not? How irrational is the prejudice that would allow plants (green fields and flowers), but not animals into Heaven." Regarding pets, he writes: "Would the same animals be in Heaven as on earth? 'Is my dead cat in Heaven?' Again, why not? God can raise up the very grass; why not cats? Though the blessed have better things to do than play with pets, the better does not exclude the lesser."
One thing is certain: Scripture provides us with a sufficient precedent for suggesting that animals will continue to exist after the return of our Lord. Isaiah 11:6-9 provides a particularly stirring image.