I have recently read Jon Katz's "The Soul of a Dog." Like all of his books I have read, it has been an enjoyable and thought provoking read.
In this book, Jon explores a difficult question, do animals have souls and thus go to heaven? He quotes several well known philosopher/theologian types (Aristotle, Aquinas, etc.) and contemporary veterinarians who entertain this question. Of course no one really knows the answer but the discussion in intriguing.
I don't have the answer either, but I have an answer that works for me.
Human's have freewill and thus can choose to accept or reject God. Animals seem more instinctually driven. What if the whole "entry into heaven requires accepting Jesus as Lord and Savior" bit only applies to humans, since they are the only ones with consciousness of choice. What if animals come with a free ticket to heaven because they are already right with God.
The Garden of Eden had animal and plant life communing with God long before humans were even on the scene. God seems to like animals.
Based on faith and hope, I believe that I will be reunited with all my animal friends in the afterlife. Although, I imagine that relationship will with them will look different than it did here on this side. The Bible indicates that in heaven relationships will be different, for example Matthew 22:30 states that we will no longer be married to the person we are with on Earth, but we will be like the angels. So, maybe something similar applies to our animal friends, we may know them, but the bond we share on this side will look different on the other side.
First Corinthians 13:12 seems to say that we will know a lot more in heaven. So, if we know more, then maybe we will be able to somehow know our animal friends more fully.
Several places in Jon's book, he makes the case for animals not entering into heaven. As I briefly entertained such a notion I was aware of feelings of intensely deep pain. I am more inclined to believe that one day I will get to more fully experience the great delight of holding and loving my dear Max again.