I cannot imagine Heaven without animals. And the Bible does say that the lion will lie down with the lamb, in God's holy mountain. I really do believe that there will be animals in Heaven.

The wolf also shall dwell with the lamb, and the leopard shall lie down with the kid; and the calf and the young lion and the fatling together; and a little child shall lead them. And the cow and the bear shall feed; their young ones shall lie down together: and the lion shall eat straw like the ox. And the sucking child shall play on the hole of the asp, and the weaned child shall put his hand on the cockatrice' den. They shall not hurt nor destroy in all my holy mountain. Isaiah 11:6-9

A pet that dies, can be a major heartbreak for a child. I love the way my mother handled this.

My mother, a kind and godly woman, taught me as a child, that the Bible does not tell us if our pets will be in Heaven, but it does tell us that there is only joy there. So if we want our pet when we get there, God will surely give it to us. I taught my children this too.

This is a tremendous comfort for a child. A child cannot understand a possibility that he or she might not remember that pet, in Heaven. Nor do I think they should be told that. There is no harm in letting a child believe they will remember the pet they love so dearly. We don't know, after all. God may arrange it so we do. And He would then, give us our pets back, because the Bible says there is no sorrow there.