Yes
How about reading Genesis 3.
Reading these verses helps us to see that God intended people and animals to eat only “green stuff”. God did not intend for people or animals to die. This has led many commentators to believe that whilst people are body, mind, soul and spirit, animals are body, mind and soul. It is the spiritual element that separates people from animals but it is the soul that links animals into, I believe, eternal life with God.
Originally, God intends for people and animals to live forever. Through sin, death was brought into this world. This corrupted creation as a whole, bringing death to people and animals. Through Jesus’ death on the cross and his bodily resurrection we can now regain eternal life. This salvation is intended for the whole of creation. The Bible tells us that one day, with the return of Jesus, God will create a new earth, with the whole of creation, animals and all.
I particularly feel that any animals that spend time with people are fulfilling their creation role, i.e. to be under people’s authority. So, if you have a dog or cat as a pet, I believe, you will be reunited with that pet in heaven. I am really looking forward to being able to say “hello” to my dogs and to go for a walk with them!
The key to all this, is that you must get to know Jesus yourself. If you want to go to meet your animals in heaven, get there yourself!
For we know that up to the present time all of creation groans with pain, like the pain of childbirth. Romans 8 v 22. Creation groans because they look for the return of Jesus. They want to be with their God, as we should be groaning as well!
Be encouraged and look forward to the day when in heaven, you will be reunited with God, with friends and with your pets.