In terms of the Bible, even what it says regarding humans living forever isn't exactly clear and is the subject of much heated debate so imagine how unclear it would be to use the Bible to find out about the eternal fate of animals. I'm sure if there was anything in there about that, people would be all over it.
As kids, the JW's used to entice us to be good so we'd live in the new system and have our very own pet Lion or Panda or Dolphin. I remember I was pretty upset when I found out that the animals in the new system wouldn't live forever. I couldn't imagine losing beloved pets for all eternity.
I wondered how God could allow the animals to grow old, get sick and and die. What did they ever do? Then I learned that the kids at school would be destroyed at armageddon if their parents didn't become JW's and even us JW children would be destroyed if our parents weren't good enough JW's. I figured that if god would kill kids just because their Mother or Father did something wrong then he surely wouldn't mind letting their pets and other animals die as well.
It was a messed up way to grow up and it left it's mark on me and it's no wonder I was plagued with anxiety until I left the JW's when I reached middle age. It was a blessing to leave all those silly man made notions about God behind.
Having had many pets over the years, I've learned (the hard way) not to project my worries and sentimental feelings onto them. Animals aren't comfortable when they are doted on too much and it makes them weird and spoiled. Unlike us, animals live in the present moment. They are hard wired to preserve themselves alive but they aren't aware that they will die one day. They are blissfully unaware of their own mortality. They do not think about the past or worry about the future. They are not sentimental about things the way we are. As long as they are warm and fed and have a place that feels safe, they are satisfied. How lucky is that??
I think you should enjoy and care for the animals that come into your life and rest assured that they are at peace and were lucky to have known you and they weren't troubled one bit about their own eternal fate and neither should you be about theirs or your own. If there is a God and he does have good things in store for mankind, there's no reason you shouldn't be part of it as well (especially if you love animals). You should do the best you can for his creation within your own scope and leave the rest in his hands. That's all you can do and that's good enough.
