What does the Bible say about animals in Heaven? Will I see my dogs or cats in Heaven?
Before we can answer your question, we need to define "heaven" according to the Bible. Heaven is not a single place according to scripture. Heaven is multiple places in the course of God's program. Those who place faith in Christ and die enter the Heavenly realm in spirit form only.
However, the Heavenly throne room is not our permanent home. At Christ's return, the saints will return to earth with Him to live in the Kingdom for 1,000 years. At that point, our "heaven" will be on Earth. During this time animals will exist on earth as they do now, but those animals won't be resurrected animals from our prior life. They will simply be new animals living in that day with mankind in harmony and without conflict:
Is. 65:17 “For behold, I create new heavens and a new earth;
And the former things will not be remembered or come to mind.
Is. 65:18 “But be glad and rejoice forever in what I create;
For behold, I create Jerusalem for rejoicing
And her people for gladness.
Is. 65:19 “I will also rejoice in Jerusalem and be glad in My people;
And there will no longer be heard in her
The voice of weeping and the sound of crying.
Is. 65:20 “No longer will there be in it an infant who lives but a few days,
Or an old man who does not live out his days;
For the youth will die at the age of one hundred
And the one who does not reach the age of one hundred
Will be thought accursed.
Is. 65:21 “They will build houses and inhabit them;
They will also plant vineyards and eat their fruit.
Is. 65:22 “They will not build and another inhabit,
They will not plant and another eat;
For as the lifetime of a tree, so will be the days of My people,
And My chosen ones will wear out the work of their hands.
Is. 65:23 “They will not labor in vain,
Or bear children for calamity;
For they are the offspring of those blessed by the LORD,
And their descendants with them.
Is. 65:24 “It will also come to pass that before they call, I will answer; and while they are still speaking, I will hear.
Is. 65:25 “The wolf and the lamb will graze together, and the lion will eat straw like the ox; and dust will be the serpent’s food. They will do no evil or harm in all My holy mountain,” says the LORD.
Notice that the Lord says in the 1,000 year kingdom to come there will be animals living, and they will lie down together in harmony. We do not know if the animals in the kingdom will include pets, but it's reasonable to assume that there will be dogs, cats and other domesticated pets among the animals in the Kingdom.
On the other hand, those animals we had before we died will not be "resurrected" to join us. The Bible teaches that all life on Earth that comes from the ground (i.e., men, animals and plants) will return to dust because of the curse God pronounced after Adam's sin in Genesis 3. Furthermore, God only gives "help" (i.e., a plan of redemption and resurrection) to men, according to the BIble. He doesn't give a way for angels (or presuambly the animal kingdom) to be redeemed from the curse, according to Hebrews 2:16. So only human beings receive new eternal bodies, and the animals we find in the Kingdom will be newly born animals, not resurrected versions of animals from this world.
So while we would love to say that all our pets will be in the Kingdom waiting for us, it's safer to assume we will have an opportunity to enjoy new pets without the worry of death or pain or suffering.