Pope Francis is having the same kind of trouble the apostle Paul had.  It’s hard to be a pastor and a theologian at the same time.  And if any remarks you make are going to be seized upon by the participants in an ongoing public controversy, it is more difficult yet.
Laura Hobgood-Oster, of Southwestern University in Georgetown, Texas, has given the matter some thought.  “The Catholic Church has never been clear on this question…Where do mosquitoes go, for God’s sake?”  You can see the whole New York Times article here.
The Pope consoled a little boy whose dog had just died.  “Paradise is open to all of God’s creatures,” said the Pope.  Presuming that by “paradise,” the Pope meant “heaven,” that gets us substantially beyond Noah’s ark, in which a breeding remnant of all species was included.  It gets us to the inclusion of all animals and, depending on just what the Pope had in mind by “creatures,” all living beings whatsoever.
This suggests a different notion of ecology that we have been working with.  I know that sounds flippant and I apologize for any offense taken, but I am trying to cut a few corners here.  So let’s imagine a celestial ecology and a terrestrial ecology.  We know pretty well how things work in our terrestrial ecology.  There is a cycle of predation such that everything preys upon something, which preys upon something, etc.  Presumably, that’s what God had in mind for our earth.  Humans have had, for many hundreds of thousands of years, our own little niche in this ecology.  We are the food for animals able to kill and eat us; we kill and eat the animals we can, or scavenge from the kills of more efficient predators.  Everything works.  It is—or used to be—stable over the long term.
I’m going to skip right by some questions that might seem to be more important.  Does “paradise” mean “heaven?”  Does “heaven” mean a place where we will all be together?  Will we care?  I’m going to go to the practical questions.
If creatures go to heaven, what do they eat?  Does grass go to heaven too, or is it just the animal kingdom?  Are Flora and Fauna going to be separated for all eternity?  Do wild animals go to heaven or just domesticated ones?  Will a dog that was abused by his owner be reunited with that master in heaven?  You see the problem.
There is simply no way to map the terrestrial ecology onto the heavenly realm without starting to giggle.  Or cry.  Woody Allen quipped, using the famous passage from Isaiah as his launching pad, that in God’s rule, “the lion will lie down with the lamb.”  Currently, Allen says, only the lion gets back up.  Woody knew, I am sure, how much more productive sheep are than lions.  Possibly, he had begun to consider how the several populations could be maintained once the cycle of predation has come untied.
When you approach the matter theologically, you have to start at the other end of the problem.  Things that have souls—the hypothetically eternal part of the entities we know—can go to heaven.  That means that if the question you really want to get answered is whether Rover has a soul, the answer will be “Yes” because you will not abide Rover being “just a piece of meat.”

Skeptics like me will now come by to ask just what you mean by the notion of “soul” and how you know Rover has one.  At present, we cannot say with any confidence what a “self” is.  It is a problem of instrumentation as well as philosophy.  I’d feel better about locating a soul if we had located the self.
We could approach the question linguistically instead.  What is “heaven.”  It is a “place” in the heavens.  The heavens are a name we give to what the atmosphere looks like from ground level.  The most fundamental meaning of “the heavens” is that they are not here; they are “there.”  They are higher.  Presumably, celestial beings are better than terrestrial ones—that would be us—and they live there.  Heaven as a place is “in the heavens,” i.e., in or beyond the sky and God is “there” because He is our heavenly Father, just as we have earthly fathers.  And heaven is eternal because it doesn’t seem to end, by contrast with everything earthly, which does seem to end.
I’ve got an idea.  Let’s not go there.  Let’s take a much more traditional notion of God and let that guide us.  Everything that follows is standard Christian theology.  It won’t get odd sounding until I get to the “Now what…?” section.  God intended us for relationship with Himself.  That is our ultimate good.  Rumor has it that He values freedom, justice, and mercy—not necessarily in that order and meaning what He defines them to mean.  God is trustworthy in the sense that He has a plan and will see it through to completion.  That’s good news for everyone who wants to be a part of the plan, for sure, and might be good news even for people who don’t believe there is a plan or who want to see the plan defeated.  We don’t know, really.
But since God is a loving God and since he will persist until the end He has in mind is reached, we can trust Him to do in our time what we need and to do with us, when our time is over, whatever is best.  This works really well if you are someone who believes that this plan God has is really the only game in town and if you are someone who wants it to succeed whatever the intermediate costs are to me and to my pets if any.
Here’s the “Now what…” part.  We can’t know about the future beyond that or even whether there is a future beyond that.  Trusting God’s plan is really just a practical way of trusting God.  That moves me well beyond the “heaven or no heaven” question.  Trusting God provided that he will admit me to heaven is only a way of making our trust contingent.  That moves me well beyond the “Fido or no Fido” question as well; also whether my parents will be there or my kids and grandkids, not to mention my stepkids and their kids.  All those possible questions are short-circuited by trusting that the God who bestowed upon us life and breath and time and agency, can be trusted even when all those run out.
That does leave a theological scrap or two left to deal with, but I would rather deal with those than be the Pope and have to console a little boy about when he is going to see his dead dog again.