My thought is yes. I think Heaven will be familiar, but amazingly better. Those who have had visions of Heaven report things that they see here - trees, mountains, cities, grass, flowers, rivers, fountains, bridges, buildings - yet indescribably beautiful, and better than earth. So, I conclude from what seems to be consistent reports, that Heaven will be like earth, but better - amazingly better. The lion shall lie down with the lamb. So, a lion does not attack. Presumably nor will mosquitoes. If a person is an etymologist on earth and LOVES insects all his life, an insect-less heaven would be a little bit of a loss. But I do not think any critters will bother us, or each other, or overpopulate an area (no locust swarms in heaven) or any other pesky thing.
On earth because our relationship with the Lord is imperfect and the people in our lives are imperfect, and we are, in many instances a pet for many can make up for a lot of the lack of love on earth. But in Heaven, there will be no lack of love, no need for pet companions. So it seems to me that domestic animals will not need to meet a need like they can here.
So that’s what I think. I also once heard an amazing story from my friend who went to to city park and talked to another mom, who told an amazing story, believable, which my friend was able to tell back to me almost verbatim. Because she has an elephant’s memory. And also, she has a gift for really listening - she can give you all the time in the world. So this woman had gown up in abuse and poverty. Her parents used to fight violently, yelling, throwing and breaking things for long periods. When that happened she would go to her room and her Guardian Angel used to play board games with her. And sometimes her angel would take her on a “trip” to Heaven, where there were other children and angels playing, and they would ride the animals. Giraffes, elephants, lions. She was much, much older before she came to realize that her life was different; that other children did not experience this. There is even more to the story, but it would take too long to write. The sheep know the shepherd, and I was completely convinced about the identity of this Shepherd.
So, yes, I think there will be animals in Heaven. Its like with food - there will be food in Heaven, and we will enjoy it, but it will be different. There won’t be a *need *to eat, like on earth. We will experience it differently in eternity.