This is a great topic, thanks for posting it @Ipsevenenabibas
We need to start with Genesis to find any kind of answer to this, and I don't want to limit it to 'pets' species, but all created animals. I will add I'm a young earth Creationist, but not sure it matters in this discussion. It was Day 5 when sea and air creatures were created. This would include the ancestors of fish, whales, dolphins and also pleisiosaurs. We classify them now into fish, mammals and reptiles but they were all created on the same day. In the same way air creatures included birds, bats, flying mammals and pterosaurs. All these day 5 creatures are the first nephesh chayyah or 'living creatures', a term not used for plants even though we consider them 'alive' today, they are more self-replicating, solar-powered food factories. The expression nephesh chayyah is used for both humans and animals and can be translated from the Hebrew as 'living soul' or 'living creature'.
Land animals were created on Day 6 (this would include the ancestors of our pets, but also animals such as dinosaurs, and of course man. Again these are 'living creatures'. The land animals were made in 2 main categories: Livestock (all domesticable animals like cattle, sheep, goats, and beasts of the earth, i.e. those that could not be domesticated. Insects don't appear to be nephesh chayyah in the Bible. Of course mankind was created in God's image unlike all the other living creatures.
Paul says "For not all flesh is the same, but there is one kind for humans, another for animals, another for birds, and another for fish." (1 Cor 15:39)
My church teaches that animals were created with souls, not identical to human souls, but souls nonetheless. Compared to, say, insects who don't.
If animals have souls then what happens to their souls upon death? Does God destroy them? Do they self-destruct? I don't know, however I think God (who let's face it, knew from the beginning how fond humans would be of various critters He made) has a plan for them, too. They don't need to accept Christ as they aren't humans who fell from their own actions. They fell with humanity and because of humanity, it's we who are to blame for that. So I tend to go with yes, animals will be in Heaven. Will our pets be part of that? I don't know, I really hope so. I think all sorts of 'living creatures' will fill Heaven, including dinosaurs, who will of course not be fierce but will be friendly as will all animals, and we'll all be vegetarian again, thankfully!
We kept pigs on a small scale and were very fond of them. But we sent them to the abattoir and ate them. Will we meet them in Heaven? If you think your dog is there, why not my pigs?
Nothing wrong with pigs being in Heaven, if cats, dogs, hamsters, horses and pet snakes are in Heaven then so will pigs! I had a pet sheep as a teen, I hope she will be there!