Better question - will we even care about pets in Heaven?
It’s said that man and wife will no longer be together, so if God has a special place in his heart for the sanctity of marriage, and doesn’t maintain it, why maintain the relationship between us and animals?
I say this as a pet lover who has lost several special friends in pets.
As my pastor friend says, God will do what is right; somehow; however He does it, it will be alright.
As it was explained to me, the "together" is referring to sex. There will be no sex in heaven because there is no need for sex in heaven.
There are too many other places in scripture that refer to us being reunited in one way or another with family and friends to think that God would, for some reason, separate man and wife.
As for the animals...this is me now, not scripture...I have come to believe that there is an energy, a consciousness, a soul, in every living creature. That is what makes it "living". Mankind has a "divine" soul, made in the image of our creator. It is special. Animals also have a type of soul, just not one in the image of God.
Energy cannot be destroyed, it can only change. When we die, the energy that animates us, our soul, joins the presence of God. Because of the nature of our soul, we will have an understanding - likely incomplete - of the glory of God. Other once living beings will be there...people we've loved, pets we loved.
So what about Hell? The Crusher Cosmology has that covered. People who have rejected God's love will continue to do so. They will not accept "a man in the sky making rules". This will mean, in death, they will be isolated from the energy, from the presence of God, in darkness, alone with the self satisfaction that they were "right", there is no Heaven.
Unless God plans to make us like Vulcans, I tend to believe we will have pets in Heaven and eternity on Earth. It’s our created nature to want to bond.