It is understandable that people who love their pets wonder if they will ever see them again.  Will God resurrect them in some form in the future?

The indication from Scripture is, No.  As an aside, a Yes would lead to a hypothetically rather absurd situation of God resurrecting your pet chicken every time you ate him for dinner.

Man has a spirit, which is not an immortal soul, but exists after the body returns to dust.  It allows God to search a man’s heart.  It gives man an intellectual capacity not found in animals.  See “What is the spirit in man?” and “Do you have an immortal soul?” 

The Bible explains that the spirit in man returns to God at the end of a man’s life. 

Ecc 12:6  Remember your Creator before the silver cord is loosed, Or the golden bowl is broken, Or the pitcher shattered at the fountain, Or the wheel broken at the well.
Ecc 12:7  Then the dust will return to the earth as it was, And the spirit will return to God who gave it.

Both animals and man return to dust when they die.

Ecc 3:18  I said in my heart, “Concerning the condition of the sons of men, God tests them, that they may see that they themselves are like animals.”
Ecc 3:19  For what happens to the sons of men also happens to animals; one thing befalls them: as one dies, so dies the other. Surely, they all have one breath; man has no advantage over animals, for all is vanity.
Ecc 3:20  All go to one place: all are from the dust, and all return to dust.

The spirit in man returns to God.  If all that is left of man when he dies is his spirit (which returns to God), then his spirit must be what God uses to resurrect a person back to life.  Animals (at least some kinds of animals) have a spirit.

Ecc 3:21  Who knows the spirit of the sons of men, which goes upward, and the spirit of the animal, which goes down to the earth?

However, the spirit of animals goes down to the earth, which indicates that God does not keep them and thus has no plans for a later resurrection of the animals.  So, it looks like animals perish and that’s it.  The understanding that beasts perish is also found in the book of Psalms.

Psa 49:20  A man who is in honor, yet does not understand, Is like the beasts that perish.

Conclusion

Will God resurrect animals?  The indication from Scripture is, No.