I am unaware of anything that says pets/animals will be available to us in Heaven. God made us in His image and requires us to acknowledge Him in order to get on the reservation list. Being God, He can do anything so we really don’t know. Since Heaven will be so great that we really won’t miss our pets (won’t even be married to a person we stayed married to for all our adult years on Earth), I really don’t see why there’s all the flap.
You are absolutely right. The "flap" comes about because many lonely people have brought an animal into their life for companionship. As such, "they" can't imagine eternity without their furry friends. Many of these individuals have no understanding of scripture; they are secularists.
Would it surprise you that this kid settles the issue once and for all, via that sweet and true story called “Heaven Is For Real”, which also has a children’s version of that book and it does show in beautiful painting style of animals being in the Kingdom.